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Simplifying 3(x + -2)(x + -2) + 4 = 52 Reorder the terms: 3(-2 + x)(x + -2) + 4 = 52 Reorder the terms: 3(-2 + x)(-2 + x) + 4 = 52 Multiply (-2 + x) * (-2 + x) 3(-2(-2 + x) + x(-2 + x)) + 4 = 52 3((-2 * -2 + x * -2) + x(-2 + x)) + 4 = 52 3((4 + -2x) + x(-2 + x)) + 4 = 52 3(4 + -2x + (-2 * x + x * x)) + 4 = 52 3(4 + -2x + (-2x + x2)) + 4 = 52 Combine like terms: -2x + -2x = -4x 3(4 + -4x + x2) + 4 = 52 (4 * 3 + -4x * 3 + x2 * 3) + 4 = 52 (12 + -12x + 3x2) + 4 = 52 Reorder the terms: 12 + 4 + -12x + 3x2 = 52 Combine like terms: 12 + 4 = 16 16 + -12x + 3x2 = 52 Solving 16 + -12x + 3x2 = 52 Solving for variable 'x'. Reorder the terms: 16 + -52 + -12x + 3x2 = 52 + -52 Combine like terms: 16 + -52 = -36 -36 + -12x + 3x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -36 + -12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-12 + -4x + x2) = 0 Factor a trinomial. 3((-2 + -1x)(6 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 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 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2Subproblem 2
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 = 6Solution
x = {-2, 6}
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