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Simplifying x(9x + 32) = 4x2 + -4x + 32 Reorder the terms: x(32 + 9x) = 4x2 + -4x + 32 (32 * x + 9x * x) = 4x2 + -4x + 32 (32x + 9x2) = 4x2 + -4x + 32 Reorder the terms: 32x + 9x2 = 32 + -4x + 4x2 Solving 32x + 9x2 = 32 + -4x + 4x2 Solving for variable 'x'. Reorder the terms: -32 + 32x + 4x + 9x2 + -4x2 = 32 + -4x + 4x2 + -32 + 4x + -4x2 Combine like terms: 32x + 4x = 36x -32 + 36x + 9x2 + -4x2 = 32 + -4x + 4x2 + -32 + 4x + -4x2 Combine like terms: 9x2 + -4x2 = 5x2 -32 + 36x + 5x2 = 32 + -4x + 4x2 + -32 + 4x + -4x2 Reorder the terms: -32 + 36x + 5x2 = 32 + -32 + -4x + 4x + 4x2 + -4x2 Combine like terms: 32 + -32 = 0 -32 + 36x + 5x2 = 0 + -4x + 4x + 4x2 + -4x2 -32 + 36x + 5x2 = -4x + 4x + 4x2 + -4x2 Combine like terms: -4x + 4x = 0 -32 + 36x + 5x2 = 0 + 4x2 + -4x2 -32 + 36x + 5x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -32 + 36x + 5x2 = 0 Factor a trinomial. (-8 + -1x)(4 + -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 '(4 + -5x)' equal to zero and attempt to solve: Simplifying 4 + -5x = 0 Solving 4 + -5x = 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 + -5x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -5x = 0 + -4 -5x = 0 + -4 Combine like terms: 0 + -4 = -4 -5x = -4 Divide each side by '-5'. x = 0.8 Simplifying x = 0.8Solution
x = {-8, 0.8}
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