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Simplifying x(8x + 8) = 3x2 + -23x + 72 Reorder the terms: x(8 + 8x) = 3x2 + -23x + 72 (8 * x + 8x * x) = 3x2 + -23x + 72 (8x + 8x2) = 3x2 + -23x + 72 Reorder the terms: 8x + 8x2 = 72 + -23x + 3x2 Solving 8x + 8x2 = 72 + -23x + 3x2 Solving for variable 'x'. Reorder the terms: -72 + 8x + 23x + 8x2 + -3x2 = 72 + -23x + 3x2 + -72 + 23x + -3x2 Combine like terms: 8x + 23x = 31x -72 + 31x + 8x2 + -3x2 = 72 + -23x + 3x2 + -72 + 23x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -72 + 31x + 5x2 = 72 + -23x + 3x2 + -72 + 23x + -3x2 Reorder the terms: -72 + 31x + 5x2 = 72 + -72 + -23x + 23x + 3x2 + -3x2 Combine like terms: 72 + -72 = 0 -72 + 31x + 5x2 = 0 + -23x + 23x + 3x2 + -3x2 -72 + 31x + 5x2 = -23x + 23x + 3x2 + -3x2 Combine like terms: -23x + 23x = 0 -72 + 31x + 5x2 = 0 + 3x2 + -3x2 -72 + 31x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -72 + 31x + 5x2 = 0 Factor a trinomial. (-8 + -1x)(9 + -5x) = 0Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve: Simplifying -8 + -1x = 0 Solving -8 + -1x = 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 + -1x = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1x = 0 + 8 -1x = 0 + 8 Combine like terms: 0 + 8 = 8 -1x = 8 Divide each side by '-1'. x = -8 Simplifying x = -8Subproblem 2
Set the factor '(9 + -5x)' equal to zero and attempt to solve: Simplifying 9 + -5x = 0 Solving 9 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -5x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -5x = 0 + -9 -5x = 0 + -9 Combine like terms: 0 + -9 = -9 -5x = -9 Divide each side by '-5'. x = 1.8 Simplifying x = 1.8Solution
x = {-8, 1.8}
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