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Simplifying 0 = 2x2 + -18x + 40 Reorder the terms: 0 = 40 + -18x + 2x2 Solving 0 = 40 + -18x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -40 = -40 -40 + 18x + -2x2 = 40 + -18x + 2x2 + -40 + 18x + -2x2 Reorder the terms: -40 + 18x + -2x2 = 40 + -40 + -18x + 18x + 2x2 + -2x2 Combine like terms: 40 + -40 = 0 -40 + 18x + -2x2 = 0 + -18x + 18x + 2x2 + -2x2 -40 + 18x + -2x2 = -18x + 18x + 2x2 + -2x2 Combine like terms: -18x + 18x = 0 -40 + 18x + -2x2 = 0 + 2x2 + -2x2 -40 + 18x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -40 + 18x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-20 + 9x + -1x2) = 0 Factor a trinomial. 2((-5 + x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 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 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {5, 4}
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