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Simplifying 126 = 2x2 + 10x + 6x + 30 Reorder the terms: 126 = 30 + 10x + 6x + 2x2 Combine like terms: 10x + 6x = 16x 126 = 30 + 16x + 2x2 Solving 126 = 30 + 16x + 2x2 Solving for variable 'x'. Combine like terms: 126 + -30 = 96 96 + -16x + -2x2 = 30 + 16x + 2x2 + -30 + -16x + -2x2 Reorder the terms: 96 + -16x + -2x2 = 30 + -30 + 16x + -16x + 2x2 + -2x2 Combine like terms: 30 + -30 = 0 96 + -16x + -2x2 = 0 + 16x + -16x + 2x2 + -2x2 96 + -16x + -2x2 = 16x + -16x + 2x2 + -2x2 Combine like terms: 16x + -16x = 0 96 + -16x + -2x2 = 0 + 2x2 + -2x2 96 + -16x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 96 + -16x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + -8x + -1x2) = 0 Factor a trinomial. 2((4 + -1x)(12 + x)) = 0 Ignore the factor 2.Subproblem 1
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 = 4Subproblem 2
Set the factor '(12 + x)' equal to zero and attempt to solve: Simplifying 12 + x = 0 Solving 12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + x = 0 + -12 x = 0 + -12 Combine like terms: 0 + -12 = -12 x = -12 Simplifying x = -12Solution
x = {4, -12}
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