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Simplifying (x + -5)(x + -5) = 2x2 + -12x + 17 Reorder the terms: (-5 + x)(x + -5) = 2x2 + -12x + 17 Reorder the terms: (-5 + x)(-5 + x) = 2x2 + -12x + 17 Multiply (-5 + x) * (-5 + x) (-5(-5 + x) + x(-5 + x)) = 2x2 + -12x + 17 ((-5 * -5 + x * -5) + x(-5 + x)) = 2x2 + -12x + 17 ((25 + -5x) + x(-5 + x)) = 2x2 + -12x + 17 (25 + -5x + (-5 * x + x * x)) = 2x2 + -12x + 17 (25 + -5x + (-5x + x2)) = 2x2 + -12x + 17 Combine like terms: -5x + -5x = -10x (25 + -10x + x2) = 2x2 + -12x + 17 Reorder the terms: 25 + -10x + x2 = 17 + -12x + 2x2 Solving 25 + -10x + x2 = 17 + -12x + 2x2 Solving for variable 'x'. Reorder the terms: 25 + -17 + -10x + 12x + x2 + -2x2 = 17 + -12x + 2x2 + -17 + 12x + -2x2 Combine like terms: 25 + -17 = 8 8 + -10x + 12x + x2 + -2x2 = 17 + -12x + 2x2 + -17 + 12x + -2x2 Combine like terms: -10x + 12x = 2x 8 + 2x + x2 + -2x2 = 17 + -12x + 2x2 + -17 + 12x + -2x2 Combine like terms: x2 + -2x2 = -1x2 8 + 2x + -1x2 = 17 + -12x + 2x2 + -17 + 12x + -2x2 Reorder the terms: 8 + 2x + -1x2 = 17 + -17 + -12x + 12x + 2x2 + -2x2 Combine like terms: 17 + -17 = 0 8 + 2x + -1x2 = 0 + -12x + 12x + 2x2 + -2x2 8 + 2x + -1x2 = -12x + 12x + 2x2 + -2x2 Combine like terms: -12x + 12x = 0 8 + 2x + -1x2 = 0 + 2x2 + -2x2 8 + 2x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 8 + 2x + -1x2 = 0 Factor a trinomial. (4 + -1x)(2 + 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 '(2 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {4, -2}
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