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Simplifying 0 = 4x2 + 18x + 20 Reorder the terms: 0 = 20 + 18x + 4x2 Solving 0 = 20 + 18x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -18x + -4x2 = 20 + 18x + 4x2 + -20 + -18x + -4x2 Reorder the terms: -20 + -18x + -4x2 = 20 + -20 + 18x + -18x + 4x2 + -4x2 Combine like terms: 20 + -20 = 0 -20 + -18x + -4x2 = 0 + 18x + -18x + 4x2 + -4x2 -20 + -18x + -4x2 = 18x + -18x + 4x2 + -4x2 Combine like terms: 18x + -18x = 0 -20 + -18x + -4x2 = 0 + 4x2 + -4x2 -20 + -18x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -20 + -18x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(10 + 9x + 2x2) = 0 Factor a trinomial. -2((5 + 2x)(2 + x)) = 0 Ignore the factor -2.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 + x)' equal to zero and attempt to solve: Simplifying 2 + x = 0 Solving 2 + x = 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 + x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + x = 0 + -2 x = 0 + -2 Combine like terms: 0 + -2 = -2 x = -2 Simplifying x = -2Solution
x = {-2.5, -2}
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