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Simplifying 40x2 + 84x + -40 = 0 Reorder the terms: -40 + 84x + 40x2 = 0 Solving -40 + 84x + 40x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 21x + 10x2) = 0 Factor a trinomial. 4((-5 + -2x)(2 + -5x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-5 + -2x)' equal to zero and attempt to solve: Simplifying -5 + -2x = 0 Solving -5 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -2x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x = 0 + 5 -2x = 0 + 5 Combine like terms: 0 + 5 = 5 -2x = 5 Divide each side by '-2'. x = -2.5 Simplifying x = -2.5Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve: Simplifying 2 + -5x = 0 Solving 2 + -5x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -5x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -5x = 0 + -2 -5x = 0 + -2 Combine like terms: 0 + -2 = -2 -5x = -2 Divide each side by '-5'. x = 0.4 Simplifying x = 0.4Solution
x = {-2.5, 0.4}
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