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Simplifying x(5x + 17) = 2x2 + -2x + 14 Reorder the terms: x(17 + 5x) = 2x2 + -2x + 14 (17 * x + 5x * x) = 2x2 + -2x + 14 (17x + 5x2) = 2x2 + -2x + 14 Reorder the terms: 17x + 5x2 = 14 + -2x + 2x2 Solving 17x + 5x2 = 14 + -2x + 2x2 Solving for variable 'x'. Reorder the terms: -14 + 17x + 2x + 5x2 + -2x2 = 14 + -2x + 2x2 + -14 + 2x + -2x2 Combine like terms: 17x + 2x = 19x -14 + 19x + 5x2 + -2x2 = 14 + -2x + 2x2 + -14 + 2x + -2x2 Combine like terms: 5x2 + -2x2 = 3x2 -14 + 19x + 3x2 = 14 + -2x + 2x2 + -14 + 2x + -2x2 Reorder the terms: -14 + 19x + 3x2 = 14 + -14 + -2x + 2x + 2x2 + -2x2 Combine like terms: 14 + -14 = 0 -14 + 19x + 3x2 = 0 + -2x + 2x + 2x2 + -2x2 -14 + 19x + 3x2 = -2x + 2x + 2x2 + -2x2 Combine like terms: -2x + 2x = 0 -14 + 19x + 3x2 = 0 + 2x2 + -2x2 -14 + 19x + 3x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -14 + 19x + 3x2 = 0 Factor a trinomial. (-7 + -1x)(2 + -3x) = 0Subproblem 1
Set the factor '(-7 + -1x)' equal to zero and attempt to solve: Simplifying -7 + -1x = 0 Solving -7 + -1x = 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 + -1x = 0 + 7 Combine like terms: -7 + 7 = 0 0 + -1x = 0 + 7 -1x = 0 + 7 Combine like terms: 0 + 7 = 7 -1x = 7 Divide each side by '-1'. x = -7 Simplifying x = -7Subproblem 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 = {-7, 0.6666666667}
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