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Simplifying 8x2 = 24x + 32 Reorder the terms: 8x2 = 32 + 24x Solving 8x2 = 32 + 24x Solving for variable 'x'. Reorder the terms: -32 + -24x + 8x2 = 32 + 24x + -32 + -24x Reorder the terms: -32 + -24x + 8x2 = 32 + -32 + 24x + -24x Combine like terms: 32 + -32 = 0 -32 + -24x + 8x2 = 0 + 24x + -24x -32 + -24x + 8x2 = 24x + -24x Combine like terms: 24x + -24x = 0 -32 + -24x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-4 + -3x + x2) = 0 Factor a trinomial. 8((-1 + -1x)(4 + -1x)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve: Simplifying -1 + -1x = 0 Solving -1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1x = 0 + 1 -1x = 0 + 1 Combine like terms: 0 + 1 = 1 -1x = 1 Divide each side by '-1'. x = -1 Simplifying x = -1Subproblem 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 = {-1, 4}
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