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Simplifying 66 = (x + 7)(x + 2) Reorder the terms: 66 = (7 + x)(x + 2) Reorder the terms: 66 = (7 + x)(2 + x) Multiply (7 + x) * (2 + x) 66 = (7(2 + x) + x(2 + x)) 66 = ((2 * 7 + x * 7) + x(2 + x)) 66 = ((14 + 7x) + x(2 + x)) 66 = (14 + 7x + (2 * x + x * x)) 66 = (14 + 7x + (2x + x2)) Combine like terms: 7x + 2x = 9x 66 = (14 + 9x + x2) Solving 66 = 14 + 9x + x2 Solving for variable 'x'. Combine like terms: 66 + -14 = 52 52 + -9x + -1x2 = 14 + 9x + x2 + -14 + -9x + -1x2 Reorder the terms: 52 + -9x + -1x2 = 14 + -14 + 9x + -9x + x2 + -1x2 Combine like terms: 14 + -14 = 0 52 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2 52 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 52 + -9x + -1x2 = 0 + x2 + -1x2 52 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 52 + -9x + -1x2 = 0 Factor a trinomial. (4 + -1x)(13 + x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(13 + x)' equal to zero and attempt to solve: Simplifying 13 + x = 0 Solving 13 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + x = 0 + -13 x = 0 + -13 Combine like terms: 0 + -13 = -13 x = -13 Simplifying x = -13Solution
x = {4, -13}
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