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Simplifying 150(100 + x)(100 + x) = 216 * 10000 Multiply (100 + x) * (100 + x) 150(100(100 + x) + x(100 + x)) = 216 * 10000 150((100 * 100 + x * 100) + x(100 + x)) = 216 * 10000 150((10000 + 100x) + x(100 + x)) = 216 * 10000 150(10000 + 100x + (100 * x + x * x)) = 216 * 10000 150(10000 + 100x + (100x + x2)) = 216 * 10000 Combine like terms: 100x + 100x = 200x 150(10000 + 200x + x2) = 216 * 10000 (10000 * 150 + 200x * 150 + x2 * 150) = 216 * 10000 (1500000 + 30000x + 150x2) = 216 * 10000 Multiply 216 * 10000 1500000 + 30000x + 150x2 = 2160000 Solving 1500000 + 30000x + 150x2 = 2160000 Solving for variable 'x'. Reorder the terms: 1500000 + -2160000 + 30000x + 150x2 = 2160000 + -2160000 Combine like terms: 1500000 + -2160000 = -660000 -660000 + 30000x + 150x2 = 2160000 + -2160000 Combine like terms: 2160000 + -2160000 = 0 -660000 + 30000x + 150x2 = 0 Factor out the Greatest Common Factor (GCF), '150'. 150(-4400 + 200x + x2) = 0 Factor a trinomial. 150((-220 + -1x)(20 + -1x)) = 0 Ignore the factor 150.Subproblem 1
Set the factor '(-220 + -1x)' equal to zero and attempt to solve: Simplifying -220 + -1x = 0 Solving -220 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '220' to each side of the equation. -220 + 220 + -1x = 0 + 220 Combine like terms: -220 + 220 = 0 0 + -1x = 0 + 220 -1x = 0 + 220 Combine like terms: 0 + 220 = 220 -1x = 220 Divide each side by '-1'. x = -220 Simplifying x = -220Subproblem 2
Set the factor '(20 + -1x)' equal to zero and attempt to solve: Simplifying 20 + -1x = 0 Solving 20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-20' to each side of the equation. 20 + -20 + -1x = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -1x = 0 + -20 -1x = 0 + -20 Combine like terms: 0 + -20 = -20 -1x = -20 Divide each side by '-1'. x = 20 Simplifying x = 20Solution
x = {-220, 20}
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