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Simplifying 3x2 + x2 = 8x + 96 Combine like terms: 3x2 + x2 = 4x2 4x2 = 8x + 96 Reorder the terms: 4x2 = 96 + 8x Solving 4x2 = 96 + 8x Solving for variable 'x'. Reorder the terms: -96 + -8x + 4x2 = 96 + 8x + -96 + -8x Reorder the terms: -96 + -8x + 4x2 = 96 + -96 + 8x + -8x Combine like terms: 96 + -96 = 0 -96 + -8x + 4x2 = 0 + 8x + -8x -96 + -8x + 4x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -96 + -8x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-24 + -2x + x2) = 0 Factor a trinomial. 4((-4 + -1x)(6 + -1x)) = 0 Ignore the factor 4.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 '(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 = {-4, 6}
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