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Simplifying x(2x + 5) = 102 Reorder the terms: x(5 + 2x) = 102 (5 * x + 2x * x) = 102 (5x + 2x2) = 102 Solving 5x + 2x2 = 102 Solving for variable 'x'. Reorder the terms: -102 + 5x + 2x2 = 102 + -102 Combine like terms: 102 + -102 = 0 -102 + 5x + 2x2 = 0 Factor a trinomial. (-17 + -2x)(6 + -1x) = 0Subproblem 1
Set the factor '(-17 + -2x)' equal to zero and attempt to solve: Simplifying -17 + -2x = 0 Solving -17 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + -2x = 0 + 17 Combine like terms: -17 + 17 = 0 0 + -2x = 0 + 17 -2x = 0 + 17 Combine like terms: 0 + 17 = 17 -2x = 17 Divide each side by '-2'. x = -8.5 Simplifying x = -8.5Subproblem 2
Set the factor '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 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 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-8.5, 6}
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