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Simplifying (x + 5)(x + -5) + 16 = (x + -3) * 2 Reorder the terms: (5 + x)(x + -5) + 16 = (x + -3) * 2 Reorder the terms: (5 + x)(-5 + x) + 16 = (x + -3) * 2 Multiply (5 + x) * (-5 + x) (5(-5 + x) + x(-5 + x)) + 16 = (x + -3) * 2 ((-5 * 5 + x * 5) + x(-5 + x)) + 16 = (x + -3) * 2 ((-25 + 5x) + x(-5 + x)) + 16 = (x + -3) * 2 (-25 + 5x + (-5 * x + x * x)) + 16 = (x + -3) * 2 (-25 + 5x + (-5x + x2)) + 16 = (x + -3) * 2 Combine like terms: 5x + -5x = 0 (-25 + 0 + x2) + 16 = (x + -3) * 2 (-25 + x2) + 16 = (x + -3) * 2 Reorder the terms: -25 + 16 + x2 = (x + -3) * 2 Combine like terms: -25 + 16 = -9 -9 + x2 = (x + -3) * 2 Reorder the terms: -9 + x2 = (-3 + x) * 2 Reorder the terms for easier multiplication: -9 + x2 = 2(-3 + x) -9 + x2 = (-3 * 2 + x * 2) -9 + x2 = (-6 + 2x) Solving -9 + x2 = -6 + 2x Solving for variable 'x'. Reorder the terms: -9 + 6 + -2x + x2 = -6 + 2x + 6 + -2x Combine like terms: -9 + 6 = -3 -3 + -2x + x2 = -6 + 2x + 6 + -2x Reorder the terms: -3 + -2x + x2 = -6 + 6 + 2x + -2x Combine like terms: -6 + 6 = 0 -3 + -2x + x2 = 0 + 2x + -2x -3 + -2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -3 + -2x + x2 = 0 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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