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Simplifying x(8x + 7) = 3x2 + -2x + 18 Reorder the terms: x(7 + 8x) = 3x2 + -2x + 18 (7 * x + 8x * x) = 3x2 + -2x + 18 (7x + 8x2) = 3x2 + -2x + 18 Reorder the terms: 7x + 8x2 = 18 + -2x + 3x2 Solving 7x + 8x2 = 18 + -2x + 3x2 Solving for variable 'x'. Reorder the terms: -18 + 7x + 2x + 8x2 + -3x2 = 18 + -2x + 3x2 + -18 + 2x + -3x2 Combine like terms: 7x + 2x = 9x -18 + 9x + 8x2 + -3x2 = 18 + -2x + 3x2 + -18 + 2x + -3x2 Combine like terms: 8x2 + -3x2 = 5x2 -18 + 9x + 5x2 = 18 + -2x + 3x2 + -18 + 2x + -3x2 Reorder the terms: -18 + 9x + 5x2 = 18 + -18 + -2x + 2x + 3x2 + -3x2 Combine like terms: 18 + -18 = 0 -18 + 9x + 5x2 = 0 + -2x + 2x + 3x2 + -3x2 -18 + 9x + 5x2 = -2x + 2x + 3x2 + -3x2 Combine like terms: -2x + 2x = 0 -18 + 9x + 5x2 = 0 + 3x2 + -3x2 -18 + 9x + 5x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -18 + 9x + 5x2 = 0 Factor a trinomial. (-3 + -1x)(6 + -5x) = 0Subproblem 1
Set the factor '(-3 + -1x)' equal to zero and attempt to solve: Simplifying -3 + -1x = 0 Solving -3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1x = 0 + 3 -1x = 0 + 3 Combine like terms: 0 + 3 = 3 -1x = 3 Divide each side by '-1'. x = -3 Simplifying x = -3Subproblem 2
Set the factor '(6 + -5x)' equal to zero and attempt to solve: Simplifying 6 + -5x = 0 Solving 6 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5x = 0 + -6 -5x = 0 + -6 Combine like terms: 0 + -6 = -6 -5x = -6 Divide each side by '-5'. x = 1.2 Simplifying x = 1.2Solution
x = {-3, 1.2}
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