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Simplifying 5x(2x + -1) + -1(2x + -1) = 0 Reorder the terms: 5x(-1 + 2x) + -1(2x + -1) = 0 (-1 * 5x + 2x * 5x) + -1(2x + -1) = 0 (-5x + 10x2) + -1(2x + -1) = 0 Reorder the terms: -5x + 10x2 + -1(-1 + 2x) = 0 -5x + 10x2 + (-1 * -1 + 2x * -1) = 0 -5x + 10x2 + (1 + -2x) = 0 Reorder the terms: 1 + -5x + -2x + 10x2 = 0 Combine like terms: -5x + -2x = -7x 1 + -7x + 10x2 = 0 Solving 1 + -7x + 10x2 = 0 Solving for variable 'x'. Factor a trinomial. (1 + -5x)(1 + -2x) = 0Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve: Simplifying 1 + -5x = 0 Solving 1 + -5x = 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 + -5x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5x = 0 + -1 -5x = 0 + -1 Combine like terms: 0 + -1 = -1 -5x = -1 Divide each side by '-5'. x = 0.2 Simplifying x = 0.2Subproblem 2
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 = 0.5Solution
x = {0.2, 0.5}
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