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Simplifying 144 + (x + 5)(x + 5) = (2x + -2)(2x + -2) Reorder the terms: 144 + (5 + x)(x + 5) = (2x + -2)(2x + -2) Reorder the terms: 144 + (5 + x)(5 + x) = (2x + -2)(2x + -2) Multiply (5 + x) * (5 + x) 144 + (5(5 + x) + x(5 + x)) = (2x + -2)(2x + -2) 144 + ((5 * 5 + x * 5) + x(5 + x)) = (2x + -2)(2x + -2) 144 + ((25 + 5x) + x(5 + x)) = (2x + -2)(2x + -2) 144 + (25 + 5x + (5 * x + x * x)) = (2x + -2)(2x + -2) 144 + (25 + 5x + (5x + x2)) = (2x + -2)(2x + -2) Combine like terms: 5x + 5x = 10x 144 + (25 + 10x + x2) = (2x + -2)(2x + -2) Combine like terms: 144 + 25 = 169 169 + 10x + x2 = (2x + -2)(2x + -2) Reorder the terms: 169 + 10x + x2 = (-2 + 2x)(2x + -2) Reorder the terms: 169 + 10x + x2 = (-2 + 2x)(-2 + 2x) Multiply (-2 + 2x) * (-2 + 2x) 169 + 10x + x2 = (-2(-2 + 2x) + 2x * (-2 + 2x)) 169 + 10x + x2 = ((-2 * -2 + 2x * -2) + 2x * (-2 + 2x)) 169 + 10x + x2 = ((4 + -4x) + 2x * (-2 + 2x)) 169 + 10x + x2 = (4 + -4x + (-2 * 2x + 2x * 2x)) 169 + 10x + x2 = (4 + -4x + (-4x + 4x2)) Combine like terms: -4x + -4x = -8x 169 + 10x + x2 = (4 + -8x + 4x2) Solving 169 + 10x + x2 = 4 + -8x + 4x2 Solving for variable 'x'. Reorder the terms: 169 + -4 + 10x + 8x + x2 + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2 Combine like terms: 169 + -4 = 165 165 + 10x + 8x + x2 + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2 Combine like terms: 10x + 8x = 18x 165 + 18x + x2 + -4x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2 Combine like terms: x2 + -4x2 = -3x2 165 + 18x + -3x2 = 4 + -8x + 4x2 + -4 + 8x + -4x2 Reorder the terms: 165 + 18x + -3x2 = 4 + -4 + -8x + 8x + 4x2 + -4x2 Combine like terms: 4 + -4 = 0 165 + 18x + -3x2 = 0 + -8x + 8x + 4x2 + -4x2 165 + 18x + -3x2 = -8x + 8x + 4x2 + -4x2 Combine like terms: -8x + 8x = 0 165 + 18x + -3x2 = 0 + 4x2 + -4x2 165 + 18x + -3x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 165 + 18x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(55 + 6x + -1x2) = 0 Factor a trinomial. 3((11 + -1x)(5 + x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(11 + -1x)' equal to zero and attempt to solve: Simplifying 11 + -1x = 0 Solving 11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-11' to each side of the equation. 11 + -11 + -1x = 0 + -11 Combine like terms: 11 + -11 = 0 0 + -1x = 0 + -11 -1x = 0 + -11 Combine like terms: 0 + -11 = -11 -1x = -11 Divide each side by '-1'. x = 11 Simplifying x = 11Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {11, -5}
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