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Simplifying 0 = -4x2 + 18x + 10 Reorder the terms: 0 = 10 + 18x + -4x2 Solving 0 = 10 + 18x + -4x2 Solving for variable 'x'. Combine like terms: 0 + -10 = -10 -10 + -18x + 4x2 = 10 + 18x + -4x2 + -10 + -18x + 4x2 Reorder the terms: -10 + -18x + 4x2 = 10 + -10 + 18x + -18x + -4x2 + 4x2 Combine like terms: 10 + -10 = 0 -10 + -18x + 4x2 = 0 + 18x + -18x + -4x2 + 4x2 -10 + -18x + 4x2 = 18x + -18x + -4x2 + 4x2 Combine like terms: 18x + -18x = 0 -10 + -18x + 4x2 = 0 + -4x2 + 4x2 -10 + -18x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -10 + -18x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -9x + 2x2) = 0 Factor a trinomial. 2((-1 + -2x)(5 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-0.5, 5}
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