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Simplifying (2x + 5) * x = 403 Reorder the terms: (5 + 2x) * x = 403 Reorder the terms for easier multiplication: x(5 + 2x) = 403 (5 * x + 2x * x) = 403 (5x + 2x2) = 403 Solving 5x + 2x2 = 403 Solving for variable 'x'. Reorder the terms: -403 + 5x + 2x2 = 403 + -403 Combine like terms: 403 + -403 = 0 -403 + 5x + 2x2 = 0 Factor a trinomial. (-31 + -2x)(13 + -1x) = 0Subproblem 1
Set the factor '(-31 + -2x)' equal to zero and attempt to solve: Simplifying -31 + -2x = 0 Solving -31 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '31' to each side of the equation. -31 + 31 + -2x = 0 + 31 Combine like terms: -31 + 31 = 0 0 + -2x = 0 + 31 -2x = 0 + 31 Combine like terms: 0 + 31 = 31 -2x = 31 Divide each side by '-2'. x = -15.5 Simplifying x = -15.5Subproblem 2
Set the factor '(13 + -1x)' equal to zero and attempt to solve: Simplifying 13 + -1x = 0 Solving 13 + -1x = 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 + -1x = 0 + -13 Combine like terms: 13 + -13 = 0 0 + -1x = 0 + -13 -1x = 0 + -13 Combine like terms: 0 + -13 = -13 -1x = -13 Divide each side by '-1'. x = 13 Simplifying x = 13Solution
x = {-15.5, 13}
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