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Simplifying (x * x) + [(x + 2)(x + 2)] = 52 Multiply x * x (x2) + [(x + 2)(x + 2)] = 52 x2 + [(x + 2)(x + 2)] = 52 Reorder the terms: x2 + [(2 + x)(x + 2)] = 52 Reorder the terms: x2 + [(2 + x)(2 + x)] = 52 Multiply (2 + x) * (2 + x) x2 + [(2(2 + x) + x(2 + x))] = 52 x2 + [((2 * 2 + x * 2) + x(2 + x))] = 52 x2 + [((4 + 2x) + x(2 + x))] = 52 x2 + [(4 + 2x + (2 * x + x * x))] = 52 x2 + [(4 + 2x + (2x + x2))] = 52 Combine like terms: 2x + 2x = 4x x2 + [(4 + 4x + x2)] = 52 x2 + [4 + 4x + x2] = 52 Remove brackets around [4 + 4x + x2] x2 + 4 + 4x + x2 = 52 Reorder the terms: 4 + 4x + x2 + x2 = 52 Combine like terms: x2 + x2 = 2x2 4 + 4x + 2x2 = 52 Solving 4 + 4x + 2x2 = 52 Solving for variable 'x'. Reorder the terms: 4 + -52 + 4x + 2x2 = 52 + -52 Combine like terms: 4 + -52 = -48 -48 + 4x + 2x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -48 + 4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-24 + 2x + x2) = 0 Factor a trinomial. 2((-6 + -1x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-6, 4}
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