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Simplifying x(7x + 31) = 2x2 + -2x + 56 Reorder the terms: x(31 + 7x) = 2x2 + -2x + 56 (31 * x + 7x * x) = 2x2 + -2x + 56 (31x + 7x2) = 2x2 + -2x + 56 Reorder the terms: 31x + 7x2 = 56 + -2x + 2x2 Solving 31x + 7x2 = 56 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: -56 + 31x + 2x + 7x2 + -2x2 = 56 + -2x + 2x2 + -56 + 2x + -2x2 Combine like terms: 31x + 2x = 33x -56 + 33x + 7x2 + -2x2 = 56 + -2x + 2x2 + -56 + 2x + -2x2 Combine like terms: 7x2 + -2x2 = 5x2 -56 + 33x + 5x2 = 56 + -2x + 2x2 + -56 + 2x + -2x2 Reorder the terms: -56 + 33x + 5x2 = 56 + -56 + -2x + 2x + 2x2 + -2x2 Combine like terms: 56 + -56 = 0 -56 + 33x + 5x2 = 0 + -2x + 2x + 2x2 + -2x2 -56 + 33x + 5x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 -56 + 33x + 5x2 = 0 + 2x2 + -2x2 -56 + 33x + 5x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -56 + 33x + 5x2 = 0 Factor a trinomial. (-8 + -1x)(7 + -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 '(7 + -5x)' equal to zero and attempt to solve: Simplifying 7 + -5x = 0 Solving 7 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -5x = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -5x = 0 + -7 -5x = 0 + -7 Combine like terms: 0 + -7 = -7 -5x = -7 Divide each side by '-5'. x = 1.4 Simplifying x = 1.4Solution
x = {-8, 1.4}
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