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Simplifying (5 + -1x)(2x + 1) = 18x Reorder the terms: (5 + -1x)(1 + 2x) = 18x Multiply (5 + -1x) * (1 + 2x) (5(1 + 2x) + -1x * (1 + 2x)) = 18x ((1 * 5 + 2x * 5) + -1x * (1 + 2x)) = 18x ((5 + 10x) + -1x * (1 + 2x)) = 18x (5 + 10x + (1 * -1x + 2x * -1x)) = 18x (5 + 10x + (-1x + -2x2)) = 18x Combine like terms: 10x + -1x = 9x (5 + 9x + -2x2) = 18x Solving 5 + 9x + -2x2 = 18x Solving for variable 'x'. Reorder the terms: 5 + 9x + -18x + -2x2 = 18x + -18x Combine like terms: 9x + -18x = -9x 5 + -9x + -2x2 = 18x + -18x Combine like terms: 18x + -18x = 0 5 + -9x + -2x2 = 0 Factor a trinomial. (1 + -2x)(5 + x) = 0Subproblem 1
Set the factor '(1 + -2x)' equal to zero and attempt to solve: Simplifying 1 + -2x = 0 Solving 1 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2x = 0 + -1 -2x = 0 + -1 Combine like terms: 0 + -1 = -1 -2x = -1 Divide each side by '-2'. x = 0.5 Simplifying x = 0.5Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve: Simplifying 5 + x = 0 Solving 5 + x = 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 + x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + x = 0 + -5 x = 0 + -5 Combine like terms: 0 + -5 = -5 x = -5 Simplifying x = -5Solution
x = {0.5, -5}
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