text: # solving equations w/ radicals and exponents problem, stuck
  
  • Aug 5th 2011, 01:03 PM
  mathmathmathmathmathmathm
  solving equations w/ radicals and exponents problem, stuck
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? thanks a bunch
  • Aug 5th 2011, 01:04 PM
  mathmathmathmathmathmathm
  Re: solving equations w/ radicals and exponents problem, stuck
  heres the orginal problem
  
  sqrt of 4 - x - sqrt of x + 6 = 2
  • Aug 5th 2011, 01:07 PM
  e^(i*pi)
  Re: solving equations w/ radicals and exponents problem, stuck
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? thanks a bunch
  
  You can square both sides:
  
  $(-6-2x)^2 = (4\sqrt{x+6})^2 \ \Leftrightarrow \ 4x^2+24x+36 = 16(x+6)$
  
  Solve for x and check for extraneous solutions using the original equation. Note that due to the domain $x \geq -6$
  
  EDIT: Your equation in the OP is fine but there is an additional domain restriction $-6 \leq x \leq 4$
  
  I've put the working to show this in a spoiler to keep the post more coherent.
  
  Spoiler:
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  heres the orginal problem
  
  $\sqrt{4 - x} - \sqrt{x + 6} = 2$
  
  $\sqrt{4-x} = 2 + \sqrt{x+6}$
  
  $4-x = 4 + 4\sqrt{x+6} + x+6 = 10 + x + 4\sqrt{x+6}$
  
  If you tidy that up a bit: $-6-2x = 2\sqrt{x+6}$
  • Aug 5th 2011, 07:45 PM
  Prove It
  Re: solving equations w/ radicals and exponents problem, stuck
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? thanks a bunch
  
  Is your equation $\displaystyle -6-2x = 4\sqrt{x} + 6$ or $\displaystyle -6-2x = 4\sqrt{x+6}$?
  • Aug 5th 2011, 09:10 PM
  BERMES39
  Re: solving equations w/ radicals and exponents problem, stuck
  Try this,
  • Aug 5th 2011, 10:04 PM
  SammyS
  Re: solving equations w/ radicals and exponents problem, stuck
  To avoid producing extraneous solutions I like the following method.
  
  $-6-2x = 4\sqrt{x+6}$ , but first, divide both sides by 2 & get rid of the terms on the left side.
  
  Starting with: $0 = x+2\sqrt{x+6}+3$
  
  now add & subtract 6 at strategic locations: $0 =x+6+2\sqrt{x+6}+3-6$
  
  $0 = (\sqrt{x+6})^2+2\sqrt{x+6}-3$
  
  Now factor: $0 = (\sqrt{x+6}+3)(\sqrt{x+6}-1)$
  
  Since $\sqrt{x+6}\ne-3$, the only solution can be $\sqrt{x+6}=1\,.$
  
  This gives x=-5 .
  • Aug 6th 2011, 05:58 AM
  mrmohamed
  Re: solving equations w/ radicals and exponents problem, stuck
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? Thanks a bunch
  
  hi all
explanation: The document contains a math question and a discussion about solving it. The user is stuck on solving an equation involving radicals and exponents, and they provide the equation and the known solution. Other users offer hints and solutions to the problem.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # solving equations w/ radicals and exponents problem, stuck
  
  • Aug 5th 2011, 01:03 PM
  mathmathmathmathmathmathm
  solving equations w/ radicals and exponents problem, stuck
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? thanks a bunch
  • Aug 5th 2011, 01:04 PM
  mathmathmathmathmathmathm
  Re: solving equations w/ radicals and exponents problem, stuck
  heres the orginal problem
  
  sqrt of 4 - x - sqrt of x + 6 = 2
  • Aug 5th 2011, 01:07 PM
  e^(i*pi)
  Re: solving equations w/ radicals and exponents problem, stuck
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? thanks a bunch
  
  You can square both sides:
  
  $(-6-2x)^2 = (4\sqrt{x+6})^2 \ \Leftrightarrow \ 4x^2+24x+36 = 16(x+6)$
  
  Solve for x and check for extraneous solutions using the original equation. Note that due to the domain $x \geq -6$
  
  EDIT: Your equation in the OP is fine but there is an additional domain restriction $-6 \leq x \leq 4$
  
  I've put the working to show this in a spoiler to keep the post more coherent.
  
  Spoiler:
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  heres the orginal problem
  
  $\sqrt{4 - x} - \sqrt{x + 6} = 2$
  
  $\sqrt{4-x} = 2 + \sqrt{x+6}$
  
  $4-x = 4 + 4\sqrt{x+6} + x+6 = 10 + x + 4\sqrt{x+6}$
  
  If you tidy that up a bit: $-6-2x = 2\sqrt{x+6}$
  • Aug 5th 2011, 07:45 PM
  Prove It
  Re: solving equations w/ radicals and exponents problem, stuck
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? thanks a bunch
  
  Is your equation $\displaystyle -6-2x = 4\sqrt{x} + 6$ or $\displaystyle -6-2x = 4\sqrt{x+6}$?
  • Aug 5th 2011, 09:10 PM
  BERMES39
  Re: solving equations w/ radicals and exponents problem, stuck
  Try this,
  • Aug 5th 2011, 10:04 PM
  SammyS
  Re: solving equations w/ radicals and exponents problem, stuck
  To avoid producing extraneous solutions I like the following method.
  
  $-6-2x = 4\sqrt{x+6}$ , but first, divide both sides by 2 & get rid of the terms on the left side.
  
  Starting with: $0 = x+2\sqrt{x+6}+3$
  
  now add & subtract 6 at strategic locations: $0 =x+6+2\sqrt{x+6}+3-6$
  
  $0 = (\sqrt{x+6})^2+2\sqrt{x+6}-3$
  
  Now factor: $0 = (\sqrt{x+6}+3)(\sqrt{x+6}-1)$
  
  Since $\sqrt{x+6}\ne-3$, the only solution can be $\sqrt{x+6}=1\,.$
  
  This gives x=-5 .
  • Aug 6th 2011, 05:58 AM
  mrmohamed
  Re: solving equations w/ radicals and exponents problem, stuck
  Quote:
  
  Originally Posted by mathmathmathmathmathmathm
  -6 - 2x = 4 times sqrt of x + 6
  
  this was a part of a larger problem but i see this is where it screws up, the answer is -5 as the solution set
  
  what ive been doin w/ problems before this one was divide that 4 in both places and it always fit nicely but not in this problem, iam really frustrated can someone gimmie a hint? Thanks a bunch
  
  hi all
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question and a discussion about solving it. The user is stuck on solving an equation involving radicals and exponents, and they provide the equation and the known solution. Other users offer hints and solutions to the problem.
  
  Label: question-and-answer