text: Use this handy tool to solve any quadratic equations given in standard form.
  
  • First, enter the coefficients a, b, and c (a≠0) of the quadratic equation ax2+bx+c=0. Make sure you have entered the correct number of digits using our sig fig calculator.
  • Next, click on the "Calculate" button and the solution will be displayed.
  
  Our quadratic equation calculator can solve quadratic equations with real or complex roots. It will calculate the discriminant D=(b2-4ac) and determine whether it is equal to, greater than, or less than zero.
  
  If the discriminant is equal to zero, the equation has one real root (called a double root); if it is greater than zero, the equation has two distinct real roots; if it is less than zero, the equation has two complex roots.
  
  x2 + x + =0
  
  The calculator uses the following formula:
  
  x = (-b ± √D) / 2a, where D = b2 - 4ac
  
  This formula calculates the solution of quadratic equations (ax2+bx+c=0) where x is unknown, a is the quadratic coefficient (a ≠ 0), b is the linear coefficient and c represents the equation's constant. The letters a, b and c are known numbers and are the quadratic equation's coefficients.
  
  For example, let's take the equation 2x2-6x+3=0, where a = 2, b = -6, and c = 3.
  
  D = b2 - 4ac = (-6)2-4·2·3 = 36-24 = 12
  
  Since the discriminant is greater than zero, the equation has two real roots. These roots are found using the quadratic formula:
  
  x(1,2) = (-b ± √D) / 2a
  
  x1 = (-b + √D) / 2a = (-(-6)+3.46) / 2·2 = 9.46 / 4 = 2.37 (rounded to 3 sig figs)
  
  x2 = (-b - √D) / 2a = (-(-6)-3.46) / 2·2 = 2.54 / 4 = 0.63 (rounded to 3 sig figs)
  
  The solution is x1=2.37, x2=0.63
explanation: The document provides a detailed explanation of how to use a quadratic equation calculator, including the steps to input coefficients, the formula used to solve quadratic equations, and an example calculation. It contains a question and an answer in the form of an example problem and its solution.
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: Use this handy tool to solve any quadratic equations given in standard form.
  
  • First, enter the coefficients a, b, and c (a≠0) of the quadratic equation ax2+bx+c=0. Make sure you have entered the correct number of digits using our sig fig calculator.
  • Next, click on the "Calculate" button and the solution will be displayed.
  
  Our quadratic equation calculator can solve quadratic equations with real or complex roots. It will calculate the discriminant D=(b2-4ac) and determine whether it is equal to, greater than, or less than zero.
  
  If the discriminant is equal to zero, the equation has one real root (called a double root); if it is greater than zero, the equation has two distinct real roots; if it is less than zero, the equation has two complex roots.
  
  x2 + x + =0
  
  The calculator uses the following formula:
  
  x = (-b ± √D) / 2a, where D = b2 - 4ac
  
  This formula calculates the solution of quadratic equations (ax2+bx+c=0) where x is unknown, a is the quadratic coefficient (a ≠ 0), b is the linear coefficient and c represents the equation's constant. The letters a, b and c are known numbers and are the quadratic equation's coefficients.
  
  For example, let's take the equation 2x2-6x+3=0, where a = 2, b = -6, and c = 3.
  
  D = b2 - 4ac = (-6)2-4·2·3 = 36-24 = 12
  
  Since the discriminant is greater than zero, the equation has two real roots. These roots are found using the quadratic formula:
  
  x(1,2) = (-b ± √D) / 2a
  
  x1 = (-b + √D) / 2a = (-(-6)+3.46) / 2·2 = 9.46 / 4 = 2.37 (rounded to 3 sig figs)
  
  x2 = (-b - √D) / 2a = (-(-6)-3.46) / 2·2 = 2.54 / 4 = 0.63 (rounded to 3 sig figs)
  
  The solution is x1=2.37, x2=0.63
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document provides a detailed explanation of how to use a quadratic equation calculator, including the steps to input coefficients, the formula used to solve quadratic equations, and an example calculation. It contains a question and an answer in the form of an example problem and its solution.
  
  Label: question-and-answer