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Simplifying (10 + 2x)(15 + 2x) = 500 Multiply (10 + 2x) * (15 + 2x) (10(15 + 2x) + 2x * (15 + 2x)) = 500 ((15 * 10 + 2x * 10) + 2x * (15 + 2x)) = 500 ((150 + 20x) + 2x * (15 + 2x)) = 500 (150 + 20x + (15 * 2x + 2x * 2x)) = 500 (150 + 20x + (30x + 4x2)) = 500 Combine like terms: 20x + 30x = 50x (150 + 50x + 4x2) = 500 Solving 150 + 50x + 4x2 = 500 Solving for variable 'x'. Reorder the terms: 150 + -500 + 50x + 4x2 = 500 + -500 Combine like terms: 150 + -500 = -350 -350 + 50x + 4x2 = 500 + -500 Combine like terms: 500 + -500 = 0 -350 + 50x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-175 + 25x + 2x2) = 0 Factor a trinomial. 2((-35 + -2x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-35 + -2x)' equal to zero and attempt to solve: Simplifying -35 + -2x = 0 Solving -35 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + -2x = 0 + 35 Combine like terms: -35 + 35 = 0 0 + -2x = 0 + 35 -2x = 0 + 35 Combine like terms: 0 + 35 = 35 -2x = 35 Divide each side by '-2'. x = -17.5 Simplifying x = -17.5Subproblem 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 = {-17.5, 5}
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