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Simplifying (15 + 2x)(10 + 2x) + -150 = 150 Multiply (15 + 2x) * (10 + 2x) (15(10 + 2x) + 2x * (10 + 2x)) + -150 = 150 ((10 * 15 + 2x * 15) + 2x * (10 + 2x)) + -150 = 150 ((150 + 30x) + 2x * (10 + 2x)) + -150 = 150 (150 + 30x + (10 * 2x + 2x * 2x)) + -150 = 150 (150 + 30x + (20x + 4x2)) + -150 = 150 Combine like terms: 30x + 20x = 50x (150 + 50x + 4x2) + -150 = 150 Reorder the terms: 150 + -150 + 50x + 4x2 = 150 Combine like terms: 150 + -150 = 0 0 + 50x + 4x2 = 150 50x + 4x2 = 150 Solving 50x + 4x2 = 150 Solving for variable 'x'. Reorder the terms: -150 + 50x + 4x2 = 150 + -150 Combine like terms: 150 + -150 = 0 -150 + 50x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-75 + 25x + 2x2) = 0 Factor a trinomial. 2((-15 + -1x)(5 + -2x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(5 + -2x)' equal to zero and attempt to solve: Simplifying 5 + -2x = 0 Solving 5 + -2x = 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 + -2x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x = 0 + -5 -2x = 0 + -5 Combine like terms: 0 + -5 = -5 -2x = -5 Divide each side by '-2'. x = 2.5 Simplifying x = 2.5Solution
x = {-15, 2.5}
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