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Simplifying 52 = x(2x + 5) Reorder the terms: 52 = x(5 + 2x) 52 = (5 * x + 2x * x) 52 = (5x + 2x2) Solving 52 = 5x + 2x2 Solving for variable 'x'. Reorder the terms: 52 + -5x + -2x2 = 5x + -5x + 2x2 + -2x2 Combine like terms: 5x + -5x = 0 52 + -5x + -2x2 = 0 + 2x2 + -2x2 52 + -5x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 52 + -5x + -2x2 = 0 Factor a trinomial. (4 + -1x)(13 + 2x) = 0Subproblem 1
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 = 4Subproblem 2
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 = -6.5Solution
x = {4, -6.5}
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