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Simplifying 10x(10x + 4) + -12(10x + -1) = 0 Reorder the terms: 10x(4 + 10x) + -12(10x + -1) = 0 (4 * 10x + 10x * 10x) + -12(10x + -1) = 0 (40x + 100x2) + -12(10x + -1) = 0 Reorder the terms: 40x + 100x2 + -12(-1 + 10x) = 0 40x + 100x2 + (-1 * -12 + 10x * -12) = 0 40x + 100x2 + (12 + -120x) = 0 Reorder the terms: 12 + 40x + -120x + 100x2 = 0 Combine like terms: 40x + -120x = -80x 12 + -80x + 100x2 = 0 Solving 12 + -80x + 100x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(3 + -20x + 25x2) = 0 Factor a trinomial. 4((1 + -5x)(3 + -5x)) = 0 Ignore the factor 4.Subproblem 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 '(3 + -5x)' equal to zero and attempt to solve: Simplifying 3 + -5x = 0 Solving 3 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -5x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -5x = 0 + -3 -5x = 0 + -3 Combine like terms: 0 + -3 = -3 -5x = -3 Divide each side by '-5'. x = 0.6 Simplifying x = 0.6Solution
x = {0.2, 0.6}
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