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Simplifying -8x + 48 = -2(x + -2)(x + -2) + 32 Reorder the terms: 48 + -8x = -2(x + -2)(x + -2) + 32 Reorder the terms: 48 + -8x = -2(-2 + x)(x + -2) + 32 Reorder the terms: 48 + -8x = -2(-2 + x)(-2 + x) + 32 Multiply (-2 + x) * (-2 + x) 48 + -8x = -2(-2(-2 + x) + x(-2 + x)) + 32 48 + -8x = -2((-2 * -2 + x * -2) + x(-2 + x)) + 32 48 + -8x = -2((4 + -2x) + x(-2 + x)) + 32 48 + -8x = -2(4 + -2x + (-2 * x + x * x)) + 32 48 + -8x = -2(4 + -2x + (-2x + x2)) + 32 Combine like terms: -2x + -2x = -4x 48 + -8x = -2(4 + -4x + x2) + 32 48 + -8x = (4 * -2 + -4x * -2 + x2 * -2) + 32 48 + -8x = (-8 + 8x + -2x2) + 32 Reorder the terms: 48 + -8x = -8 + 32 + 8x + -2x2 Combine like terms: -8 + 32 = 24 48 + -8x = 24 + 8x + -2x2 Solving 48 + -8x = 24 + 8x + -2x2 Solving for variable 'x'. Reorder the terms: 48 + -24 + -8x + -8x + 2x2 = 24 + 8x + -2x2 + -24 + -8x + 2x2 Combine like terms: 48 + -24 = 24 24 + -8x + -8x + 2x2 = 24 + 8x + -2x2 + -24 + -8x + 2x2 Combine like terms: -8x + -8x = -16x 24 + -16x + 2x2 = 24 + 8x + -2x2 + -24 + -8x + 2x2 Reorder the terms: 24 + -16x + 2x2 = 24 + -24 + 8x + -8x + -2x2 + 2x2 Combine like terms: 24 + -24 = 0 24 + -16x + 2x2 = 0 + 8x + -8x + -2x2 + 2x2 24 + -16x + 2x2 = 8x + -8x + -2x2 + 2x2 Combine like terms: 8x + -8x = 0 24 + -16x + 2x2 = 0 + -2x2 + 2x2 24 + -16x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 24 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -8x + x2) = 0 Factor a trinomial. 2((2 + -1x)(6 + -1x)) = 0 Ignore the factor 2.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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