Factoring with the Quadratic Formula m2 – 5m – 14 = 0 (m-7)(m+2) = 0 M =7, -2 Solve the same problem using the quadratic formula. A represents the first coefficient (1) B represents the second coefficient (-5) C represents the constant (-14) Factoring by Completing the Square (Purple Math) + 6x 7 = 0 This is the original equation. x2 – + 6x = 7 Move the loose number over to the other side. x2 x-term Take half of the (that is, divide it by two) (and don't forget the sign!), and square it. Add this square to both sides of the equation. Convert the left-hand side to squared (x + 3)2 = 16 form. Simplify the right-hand side. "±" Square-root both sides. Remember to do on + 3 = ± 4 x the right-hand side. = 3 ± 4 x – "±" Solve for "x =". Remember that the gives you = 3 4, + 4 – – –3 two solutions. Simplify as necessary. = +1 –7, Corresponding Worksheet: Using the Quadratic Formula, Completing the Square Combining Like Terms
Factoring with the Quadratic Formula m2 – 5m – 14 = 0 (m-7)(m+2) = 0 M =7, -2 Solve the same problem using the quadratic formula. A represents the first coefficient (1) B represents the second coefficient (-5) C represents the constant (-14) Factoring by Completing the Square (Purple Math) This is the original equation. x2 + 6x – 7 = 0 Move the loose number over to the other side. x2 + 6x = 7 Take half of the x-term (that is, divide it by two) (and don't forget the sign!), and square it. Add this square to both sides of the equation. Convert the left-hand side to squared form. Simplify the right-hand side. (x + 3)2 = 16 Square-root both sides. Remember to do "±" on the right-hand side. x + 3 = ± 4 Solve for "x =". Remember that the "±" gives you two solutions. Simplify as necessary. x = – 3 ± 4 = – 3 – 4, –3 + 4 = –7, +1 Corresponding Worksheet: Using the Quadratic Formula, Completing the Square Combining Like Terms
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