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Simplifying 2x(25x2 + -50x + 25) + -10x2(5 + -5x) = 0 Reorder the terms: 2x(25 + -50x + 25x2) + -10x2(5 + -5x) = 0 (25 * 2x + -50x * 2x + 25x2 * 2x) + -10x2(5 + -5x) = 0 (50x + -100x2 + 50x3) + -10x2(5 + -5x) = 0 50x + -100x2 + 50x3 + (5 * -10x2 + -5x * -10x2) = 0 50x + -100x2 + 50x3 + (-50x2 + 50x3) = 0 Reorder the terms: 50x + -100x2 + -50x2 + 50x3 + 50x3 = 0 Combine like terms: -100x2 + -50x2 = -150x2 50x + -150x2 + 50x3 + 50x3 = 0 Combine like terms: 50x3 + 50x3 = 100x3 50x + -150x2 + 100x3 = 0 Solving 50x + -150x2 + 100x3 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '50x'. 50x(1 + -3x + 2x2) = 0 Factor a trinomial. 50x((1 + -2x)(1 + -1x)) = 0 Ignore the factor 50.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 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 = 0.5Subproblem 3
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 = {0, 0.5, 1}
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