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Simplifying 9x2 + 24x = x2 + 32x Reorder the terms: 24x + 9x2 = x2 + 32x Reorder the terms: 24x + 9x2 = 32x + x2 Solving 24x + 9x2 = 32x + x2 Solving for variable 'x'. Reorder the terms: 24x + -32x + 9x2 + -1x2 = 32x + x2 + -32x + -1x2 Combine like terms: 24x + -32x = -8x -8x + 9x2 + -1x2 = 32x + x2 + -32x + -1x2 Combine like terms: 9x2 + -1x2 = 8x2 -8x + 8x2 = 32x + x2 + -32x + -1x2 Reorder the terms: -8x + 8x2 = 32x + -32x + x2 + -1x2 Combine like terms: 32x + -32x = 0 -8x + 8x2 = 0 + x2 + -1x2 -8x + 8x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -8x + 8x2 = 0 Factor out the Greatest Common Factor (GCF), '8x'. 8x(-1 + x) = 0 Ignore the factor 8.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(-1 + x)' equal to zero and attempt to solve: Simplifying -1 + x = 0 Solving -1 + x = 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 + x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + x = 0 + 1 x = 0 + 1 Combine like terms: 0 + 1 = 1 x = 1 Simplifying x = 1Solution
x = {0, 1}
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