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Simplifying 100x2 + -40x + 4 = 9 Reorder the terms: 4 + -40x + 100x2 = 9 Solving 4 + -40x + 100x2 = 9 Solving for variable 'x'. Reorder the terms: 4 + -9 + -40x + 100x2 = 9 + -9 Combine like terms: 4 + -9 = -5 -5 + -40x + 100x2 = 9 + -9 Combine like terms: 9 + -9 = 0 -5 + -40x + 100x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-1 + -8x + 20x2) = 0 Factor a trinomial. 5((-1 + -10x)(1 + -2x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-1 + -10x)' equal to zero and attempt to solve: Simplifying -1 + -10x = 0 Solving -1 + -10x = 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 + -10x = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -10x = 0 + 1 -10x = 0 + 1 Combine like terms: 0 + 1 = 1 -10x = 1 Divide each side by '-10'. x = -0.1 Simplifying x = -0.1Subproblem 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 = {-0.1, 0.5}
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