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Simplifying (x + 2)(x + -2) = 2(x + 5) + 21 Reorder the terms: (2 + x)(x + -2) = 2(x + 5) + 21 Reorder the terms: (2 + x)(-2 + x) = 2(x + 5) + 21 Multiply (2 + x) * (-2 + x) (2(-2 + x) + x(-2 + x)) = 2(x + 5) + 21 ((-2 * 2 + x * 2) + x(-2 + x)) = 2(x + 5) + 21 ((-4 + 2x) + x(-2 + x)) = 2(x + 5) + 21 (-4 + 2x + (-2 * x + x * x)) = 2(x + 5) + 21 (-4 + 2x + (-2x + x2)) = 2(x + 5) + 21 Combine like terms: 2x + -2x = 0 (-4 + 0 + x2) = 2(x + 5) + 21 (-4 + x2) = 2(x + 5) + 21 Reorder the terms: -4 + x2 = 2(5 + x) + 21 -4 + x2 = (5 * 2 + x * 2) + 21 -4 + x2 = (10 + 2x) + 21 Reorder the terms: -4 + x2 = 10 + 21 + 2x Combine like terms: 10 + 21 = 31 -4 + x2 = 31 + 2x Solving -4 + x2 = 31 + 2x Solving for variable 'x'. Reorder the terms: -4 + -31 + -2x + x2 = 31 + 2x + -31 + -2x Combine like terms: -4 + -31 = -35 -35 + -2x + x2 = 31 + 2x + -31 + -2x Reorder the terms: -35 + -2x + x2 = 31 + -31 + 2x + -2x Combine like terms: 31 + -31 = 0 -35 + -2x + x2 = 0 + 2x + -2x -35 + -2x + x2 = 2x + -2x Combine like terms: 2x + -2x = 0 -35 + -2x + x2 = 0 Factor a trinomial. (-5 + -1x)(7 + -1x) = 0Subproblem 1
Set the factor '(-5 + -1x)' equal to zero and attempt to solve: Simplifying -5 + -1x = 0 Solving -5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1x = 0 + 5 -1x = 0 + 5 Combine like terms: 0 + 5 = 5 -1x = 5 Divide each side by '-1'. x = -5 Simplifying x = -5Subproblem 2
Set the factor '(7 + -1x)' equal to zero and attempt to solve: Simplifying 7 + -1x = 0 Solving 7 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1x = 0 + -7 -1x = 0 + -7 Combine like terms: 0 + -7 = -7 -1x = -7 Divide each side by '-1'. x = 7 Simplifying x = 7Solution
x = {-5, 7}
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