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Simplifying (x + 7)(x + 7) = 2x2 + 20x + 57 Reorder the terms: (7 + x)(x + 7) = 2x2 + 20x + 57 Reorder the terms: (7 + x)(7 + x) = 2x2 + 20x + 57 Multiply (7 + x) * (7 + x) (7(7 + x) + x(7 + x)) = 2x2 + 20x + 57 ((7 * 7 + x * 7) + x(7 + x)) = 2x2 + 20x + 57 ((49 + 7x) + x(7 + x)) = 2x2 + 20x + 57 (49 + 7x + (7 * x + x * x)) = 2x2 + 20x + 57 (49 + 7x + (7x + x2)) = 2x2 + 20x + 57 Combine like terms: 7x + 7x = 14x (49 + 14x + x2) = 2x2 + 20x + 57 Reorder the terms: 49 + 14x + x2 = 57 + 20x + 2x2 Solving 49 + 14x + x2 = 57 + 20x + 2x2 Solving for variable 'x'. Reorder the terms: 49 + -57 + 14x + -20x + x2 + -2x2 = 57 + 20x + 2x2 + -57 + -20x + -2x2 Combine like terms: 49 + -57 = -8 -8 + 14x + -20x + x2 + -2x2 = 57 + 20x + 2x2 + -57 + -20x + -2x2 Combine like terms: 14x + -20x = -6x -8 + -6x + x2 + -2x2 = 57 + 20x + 2x2 + -57 + -20x + -2x2 Combine like terms: x2 + -2x2 = -1x2 -8 + -6x + -1x2 = 57 + 20x + 2x2 + -57 + -20x + -2x2 Reorder the terms: -8 + -6x + -1x2 = 57 + -57 + 20x + -20x + 2x2 + -2x2 Combine like terms: 57 + -57 = 0 -8 + -6x + -1x2 = 0 + 20x + -20x + 2x2 + -2x2 -8 + -6x + -1x2 = 20x + -20x + 2x2 + -2x2 Combine like terms: 20x + -20x = 0 -8 + -6x + -1x2 = 0 + 2x2 + -2x2 -8 + -6x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + -6x + -1x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(8 + 6x + x2) = 0 Factor a trinomial. -1((4 + x)(2 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 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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