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Simplifying (100 + x)(150 + x) = 15000 Multiply (100 + x) * (150 + x) (100(150 + x) + x(150 + x)) = 15000 ((150 * 100 + x * 100) + x(150 + x)) = 15000 ((15000 + 100x) + x(150 + x)) = 15000 (15000 + 100x + (150 * x + x * x)) = 15000 (15000 + 100x + (150x + x2)) = 15000 Combine like terms: 100x + 150x = 250x (15000 + 250x + x2) = 15000 Add '-15000' to each side of the equation. 15000 + 250x + -15000 + x2 = 15000 + -15000 Reorder the terms: 15000 + -15000 + 250x + x2 = 15000 + -15000 Combine like terms: 15000 + -15000 = 0 0 + 250x + x2 = 15000 + -15000 250x + x2 = 15000 + -15000 Combine like terms: 15000 + -15000 = 0 250x + x2 = 0 Solving 250x + x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), 'x'. x(250 + x) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(250 + x)' equal to zero and attempt to solve: Simplifying 250 + x = 0 Solving 250 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-250' to each side of the equation. 250 + -250 + x = 0 + -250 Combine like terms: 250 + -250 = 0 0 + x = 0 + -250 x = 0 + -250 Combine like terms: 0 + -250 = -250 x = -250 Simplifying x = -250Solution
x = {0, -250}
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