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Simplifying (x + 2)(x + 2) + -5(x + 2) = x + 57 Reorder the terms: (2 + x)(x + 2) + -5(x + 2) = x + 57 Reorder the terms: (2 + x)(2 + x) + -5(x + 2) = x + 57 Multiply (2 + x) * (2 + x) (2(2 + x) + x(2 + x)) + -5(x + 2) = x + 57 ((2 * 2 + x * 2) + x(2 + x)) + -5(x + 2) = x + 57 ((4 + 2x) + x(2 + x)) + -5(x + 2) = x + 57 (4 + 2x + (2 * x + x * x)) + -5(x + 2) = x + 57 (4 + 2x + (2x + x2)) + -5(x + 2) = x + 57 Combine like terms: 2x + 2x = 4x (4 + 4x + x2) + -5(x + 2) = x + 57 Reorder the terms: 4 + 4x + x2 + -5(2 + x) = x + 57 4 + 4x + x2 + (2 * -5 + x * -5) = x + 57 4 + 4x + x2 + (-10 + -5x) = x + 57 Reorder the terms: 4 + -10 + 4x + -5x + x2 = x + 57 Combine like terms: 4 + -10 = -6 -6 + 4x + -5x + x2 = x + 57 Combine like terms: 4x + -5x = -1x -6 + -1x + x2 = x + 57 Reorder the terms: -6 + -1x + x2 = 57 + x Solving -6 + -1x + x2 = 57 + x Solving for variable 'x'. Reorder the terms: -6 + -57 + -1x + -1x + x2 = 57 + x + -57 + -1x Combine like terms: -6 + -57 = -63 -63 + -1x + -1x + x2 = 57 + x + -57 + -1x Combine like terms: -1x + -1x = -2x -63 + -2x + x2 = 57 + x + -57 + -1x Reorder the terms: -63 + -2x + x2 = 57 + -57 + x + -1x Combine like terms: 57 + -57 = 0 -63 + -2x + x2 = 0 + x + -1x -63 + -2x + x2 = x + -1x Combine like terms: x + -1x = 0 -63 + -2x + x2 = 0 Factor a trinomial. (-7 + -1x)(9 + -1x) = 0Subproblem 1
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 = -7Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-7, 9}
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