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Simplifying x(5x + 8) = 2x2 + -11x + 40 Reorder the terms: x(8 + 5x) = 2x2 + -11x + 40 (8 * x + 5x * x) = 2x2 + -11x + 40 (8x + 5x2) = 2x2 + -11x + 40 Reorder the terms: 8x + 5x2 = 40 + -11x + 2x2 Solving 8x + 5x2 = 40 + -11x + 2x2 Solving for variable 'x'. Reorder the terms: -40 + 8x + 11x + 5x2 + -2x2 = 40 + -11x + 2x2 + -40 + 11x + -2x2 Combine like terms: 8x + 11x = 19x -40 + 19x + 5x2 + -2x2 = 40 + -11x + 2x2 + -40 + 11x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -40 + 19x + 3x2 = 40 + -11x + 2x2 + -40 + 11x + -2x2 Reorder the terms: -40 + 19x + 3x2 = 40 + -40 + -11x + 11x + 2x2 + -2x2 Combine like terms: 40 + -40 = 0 -40 + 19x + 3x2 = 0 + -11x + 11x + 2x2 + -2x2 -40 + 19x + 3x2 = -11x + 11x + 2x2 + -2x2 Combine like terms: -11x + 11x = 0 -40 + 19x + 3x2 = 0 + 2x2 + -2x2 -40 + 19x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -40 + 19x + 3x2 = 0 Factor a trinomial. (-8 + -1x)(5 + -3x) = 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 '(5 + -3x)' equal to zero and attempt to solve: Simplifying 5 + -3x = 0 Solving 5 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -3x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -3x = 0 + -5 -3x = 0 + -5 Combine like terms: 0 + -5 = -5 -3x = -5 Divide each side by '-3'. x = 1.666666667 Simplifying x = 1.666666667Solution
x = {-8, 1.666666667}
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