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Simplifying (x + 5)(x + 5) + -12(x + 5) + 32 = 0 Reorder the terms: (5 + x)(x + 5) + -12(x + 5) + 32 = 0 Reorder the terms: (5 + x)(5 + x) + -12(x + 5) + 32 = 0 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) + -12(x + 5) + 32 = 0 ((5 * 5 + x * 5) + x(5 + x)) + -12(x + 5) + 32 = 0 ((25 + 5x) + x(5 + x)) + -12(x + 5) + 32 = 0 (25 + 5x + (5 * x + x * x)) + -12(x + 5) + 32 = 0 (25 + 5x + (5x + x2)) + -12(x + 5) + 32 = 0 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) + -12(x + 5) + 32 = 0 Reorder the terms: 25 + 10x + x2 + -12(5 + x) + 32 = 0 25 + 10x + x2 + (5 * -12 + x * -12) + 32 = 0 25 + 10x + x2 + (-60 + -12x) + 32 = 0 Reorder the terms: 25 + -60 + 32 + 10x + -12x + x2 = 0 Combine like terms: 25 + -60 = -35 -35 + 32 + 10x + -12x + x2 = 0 Combine like terms: -35 + 32 = -3 -3 + 10x + -12x + x2 = 0 Combine like terms: 10x + -12x = -2x -3 + -2x + x2 = 0 Solving -3 + -2x + x2 = 0 Solving for variable 'x'. Factor a trinomial. (-1 + -1x)(3 + -1x) = 0Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-1, 3}
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