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Simplifying (10 + x) * x = (90 + x) Reorder the terms for easier multiplication: x(10 + x) = (90 + x) (10 * x + x * x) = (90 + x) (10x + x2) = (90 + x) Remove parenthesis around (90 + x) 10x + x2 = 90 + x Solving 10x + x2 = 90 + x Solving for variable 'x'. Reorder the terms: -90 + 10x + -1x + x2 = 90 + x + -90 + -1x Combine like terms: 10x + -1x = 9x -90 + 9x + x2 = 90 + x + -90 + -1x Reorder the terms: -90 + 9x + x2 = 90 + -90 + x + -1x Combine like terms: 90 + -90 = 0 -90 + 9x + x2 = 0 + x + -1x -90 + 9x + x2 = x + -1x Combine like terms: x + -1x = 0 -90 + 9x + x2 = 0 Factor a trinomial. (-15 + -1x)(6 + -1x) = 0Subproblem 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 '(6 + -1x)' equal to zero and attempt to solve: Simplifying 6 + -1x = 0 Solving 6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1x = 0 + -6 -1x = 0 + -6 Combine like terms: 0 + -6 = -6 -1x = -6 Divide each side by '-1'. x = 6 Simplifying x = 6Solution
x = {-15, 6}
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