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Simplifying x(2x + 30) = 500 Reorder the terms: x(30 + 2x) = 500 (30 * x + 2x * x) = 500 (30x + 2x2) = 500 Solving 30x + 2x2 = 500 Solving for variable 'x'. Reorder the terms: -500 + 30x + 2x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -500 + 30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-250 + 15x + x2) = 0 Factor a trinomial. 2((-25 + -1x)(10 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-25 + -1x)' equal to zero and attempt to solve: Simplifying -25 + -1x = 0 Solving -25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '25' to each side of the equation. -25 + 25 + -1x = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -1x = 0 + 25 -1x = 0 + 25 Combine like terms: 0 + 25 = 25 -1x = 25 Divide each side by '-1'. x = -25 Simplifying x = -25Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-25, 10}
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