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Simplifying (25 + x)(600 + -50x) = 0 Multiply (25 + x) * (600 + -50x) (25(600 + -50x) + x(600 + -50x)) = 0 ((600 * 25 + -50x * 25) + x(600 + -50x)) = 0 ((15000 + -1250x) + x(600 + -50x)) = 0 (15000 + -1250x + (600 * x + -50x * x)) = 0 (15000 + -1250x + (600x + -50x2)) = 0 Combine like terms: -1250x + 600x = -650x (15000 + -650x + -50x2) = 0 Solving 15000 + -650x + -50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50'. 50(300 + -13x + -1x2) = 0 Factor a trinomial. 50((12 + -1x)(25 + x)) = 0 Ignore the factor 50.Subproblem 1
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve: Simplifying 25 + x = 0 Solving 25 + x = 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 + x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + x = 0 + -25 x = 0 + -25 Combine like terms: 0 + -25 = -25 x = -25 Simplifying x = -25Solution
x = {12, -25}
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