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Simplifying 25x(x + -1) = -5(5 + -1x) + 20x Reorder the terms: 25x(-1 + x) = -5(5 + -1x) + 20x (-1 * 25x + x * 25x) = -5(5 + -1x) + 20x (-25x + 25x2) = -5(5 + -1x) + 20x -25x + 25x2 = (5 * -5 + -1x * -5) + 20x -25x + 25x2 = (-25 + 5x) + 20x Combine like terms: 5x + 20x = 25x -25x + 25x2 = -25 + 25x Solving -25x + 25x2 = -25 + 25x Solving for variable 'x'. Reorder the terms: 25 + -25x + -25x + 25x2 = -25 + 25x + 25 + -25x Combine like terms: -25x + -25x = -50x 25 + -50x + 25x2 = -25 + 25x + 25 + -25x Reorder the terms: 25 + -50x + 25x2 = -25 + 25 + 25x + -25x Combine like terms: -25 + 25 = 0 25 + -50x + 25x2 = 0 + 25x + -25x 25 + -50x + 25x2 = 25x + -25x Combine like terms: 25x + -25x = 0 25 + -50x + 25x2 = 0 Factor out the Greatest Common Factor (GCF), '25'. 25(1 + -2x + x2) = 0 Factor a trinomial. 25((1 + -1x)(1 + -1x)) = 0 Ignore the factor 25.Subproblem 1
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 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 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {1, 1}
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