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Simplifying x(2x + 3) = 65 Reorder the terms: x(3 + 2x) = 65 (3 * x + 2x * x) = 65 (3x + 2x2) = 65 Solving 3x + 2x2 = 65 Solving for variable 'x'. Reorder the terms: -65 + 3x + 2x2 = 65 + -65 Combine like terms: 65 + -65 = 0 -65 + 3x + 2x2 = 0 Factor a trinomial. (-13 + -2x)(5 + -1x) = 0Subproblem 1
Set the factor '(-13 + -2x)' equal to zero and attempt to solve: Simplifying -13 + -2x = 0 Solving -13 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '13' to each side of the equation. -13 + 13 + -2x = 0 + 13 Combine like terms: -13 + 13 = 0 0 + -2x = 0 + 13 -2x = 0 + 13 Combine like terms: 0 + 13 = 13 -2x = 13 Divide each side by '-2'. x = -6.5 Simplifying x = -6.5Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-6.5, 5}
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