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Simplifying x2 + (x + 2)(x + 2) = 130 Reorder the terms: x2 + (2 + x)(x + 2) = 130 Reorder the terms: x2 + (2 + x)(2 + x) = 130 Multiply (2 + x) * (2 + x) x2 + (2(2 + x) + x(2 + x)) = 130 x2 + ((2 * 2 + x * 2) + x(2 + x)) = 130 x2 + ((4 + 2x) + x(2 + x)) = 130 x2 + (4 + 2x + (2 * x + x * x)) = 130 x2 + (4 + 2x + (2x + x2)) = 130 Combine like terms: 2x + 2x = 4x x2 + (4 + 4x + x2) = 130 Reorder the terms: 4 + 4x + x2 + x2 = 130 Combine like terms: x2 + x2 = 2x2 4 + 4x + 2x2 = 130 Solving 4 + 4x + 2x2 = 130 Solving for variable 'x'. Reorder the terms: 4 + -130 + 4x + 2x2 = 130 + -130 Combine like terms: 4 + -130 = -126 -126 + 4x + 2x2 = 130 + -130 Combine like terms: 130 + -130 = 0 -126 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-63 + 2x + x2) = 0 Factor a trinomial. 2((-9 + -1x)(7 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -9Subproblem 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 = {-9, 7}
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