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Simplifying x(5x + 9) = 2x2 + -13x + 16 Reorder the terms: x(9 + 5x) = 2x2 + -13x + 16 (9 * x + 5x * x) = 2x2 + -13x + 16 (9x + 5x2) = 2x2 + -13x + 16 Reorder the terms: 9x + 5x2 = 16 + -13x + 2x2 Solving 9x + 5x2 = 16 + -13x + 2x2 Solving for variable 'x'. Reorder the terms: -16 + 9x + 13x + 5x2 + -2x2 = 16 + -13x + 2x2 + -16 + 13x + -2x2 Combine like terms: 9x + 13x = 22x -16 + 22x + 5x2 + -2x2 = 16 + -13x + 2x2 + -16 + 13x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -16 + 22x + 3x2 = 16 + -13x + 2x2 + -16 + 13x + -2x2 Reorder the terms: -16 + 22x + 3x2 = 16 + -16 + -13x + 13x + 2x2 + -2x2 Combine like terms: 16 + -16 = 0 -16 + 22x + 3x2 = 0 + -13x + 13x + 2x2 + -2x2 -16 + 22x + 3x2 = -13x + 13x + 2x2 + -2x2 Combine like terms: -13x + 13x = 0 -16 + 22x + 3x2 = 0 + 2x2 + -2x2 -16 + 22x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -16 + 22x + 3x2 = 0 Factor a trinomial. (-8 + -1x)(2 + -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 '(2 + -3x)' equal to zero and attempt to solve: Simplifying 2 + -3x = 0 Solving 2 + -3x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3x = 0 + -2 -3x = 0 + -2 Combine like terms: 0 + -2 = -2 -3x = -2 Divide each side by '-3'. x = 0.6666666667 Simplifying x = 0.6666666667Solution
x = {-8, 0.6666666667}
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