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Simplifying 81x + 20 = x(90 + -1x) Reorder the terms: 20 + 81x = x(90 + -1x) 20 + 81x = (90 * x + -1x * x) 20 + 81x = (90x + -1x2) Solving 20 + 81x = 90x + -1x2 Solving for variable 'x'. Combine like terms: 81x + -90x = -9x 20 + -9x + x2 = 90x + -1x2 + -90x + x2 Reorder the terms: 20 + -9x + x2 = 90x + -90x + -1x2 + x2 Combine like terms: 90x + -90x = 0 20 + -9x + x2 = 0 + -1x2 + x2 20 + -9x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 20 + -9x + x2 = 0 Factor a trinomial. (4 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {4, 5}
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