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Simplifying 12x = 32 + x2 Solving 12x = 32 + x2 Solving for variable 'x'. Reorder the terms: -32 + 12x + -1x2 = 32 + x2 + -32 + -1x2 Reorder the terms: -32 + 12x + -1x2 = 32 + -32 + x2 + -1x2 Combine like terms: 32 + -32 = 0 -32 + 12x + -1x2 = 0 + x2 + -1x2 -32 + 12x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -32 + 12x + -1x2 = 0 Factor a trinomial. (-8 + x)(4 + -1x) = 0Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve: Simplifying -8 + x = 0 Solving -8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + x = 0 + 8 x = 0 + 8 Combine like terms: 0 + 8 = 8 x = 8 Simplifying x = 8Subproblem 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 = {8, 4}
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