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Simplifying (2x + 5)(x) = 52 Reorder the terms: (5 + 2x)(x) = 52 Reorder the terms for easier multiplication: x(5 + 2x) = 52 (5 * x + 2x * x) = 52 (5x + 2x2) = 52 Solving 5x + 2x2 = 52 Solving for variable 'x'. Reorder the terms: -52 + 5x + 2x2 = 52 + -52 Combine like terms: 52 + -52 = 0 -52 + 5x + 2x2 = 0 Factor a trinomial. (-13 + -2x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-6.5, 4}
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