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Simplifying (50 + x)(x) = 5000 Reorder the terms for easier multiplication: x(50 + x) = 5000 (50 * x + x * x) = 5000 (50x + x2) = 5000 Solving 50x + x2 = 5000 Solving for variable 'x'. Reorder the terms: -5000 + 50x + x2 = 5000 + -5000 Combine like terms: 5000 + -5000 = 0 -5000 + 50x + x2 = 0 Factor a trinomial. (-100 + -1x)(50 + -1x) = 0Subproblem 1
Set the factor '(-100 + -1x)' equal to zero and attempt to solve: Simplifying -100 + -1x = 0 Solving -100 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + -1x = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -1x = 0 + 100 -1x = 0 + 100 Combine like terms: 0 + 100 = 100 -1x = 100 Divide each side by '-1'. x = -100 Simplifying x = -100Subproblem 2
Set the factor '(50 + -1x)' equal to zero and attempt to solve: Simplifying 50 + -1x = 0 Solving 50 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-50' to each side of the equation. 50 + -50 + -1x = 0 + -50 Combine like terms: 50 + -50 = 0 0 + -1x = 0 + -50 -1x = 0 + -50 Combine like terms: 0 + -50 = -50 -1x = -50 Divide each side by '-1'. x = 50 Simplifying x = 50Solution
x = {-100, 50}
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