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Simplifying 5(16x2 + 24x + 9) = 20 Reorder the terms: 5(9 + 24x + 16x2) = 20 (9 * 5 + 24x * 5 + 16x2 * 5) = 20 (45 + 120x + 80x2) = 20 Solving 45 + 120x + 80x2 = 20 Solving for variable 'x'. Reorder the terms: 45 + -20 + 120x + 80x2 = 20 + -20 Combine like terms: 45 + -20 = 25 25 + 120x + 80x2 = 20 + -20 Combine like terms: 20 + -20 = 0 25 + 120x + 80x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(5 + 24x + 16x2) = 0 Factor a trinomial. 5((5 + 4x)(1 + 4x)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(5 + 4x)' equal to zero and attempt to solve: Simplifying 5 + 4x = 0 Solving 5 + 4x = 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 + 4x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 4x = 0 + -5 4x = 0 + -5 Combine like terms: 0 + -5 = -5 4x = -5 Divide each side by '4'. x = -1.25 Simplifying x = -1.25Subproblem 2
Set the factor '(1 + 4x)' equal to zero and attempt to solve: Simplifying 1 + 4x = 0 Solving 1 + 4x = 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 + 4x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 4x = 0 + -1 4x = 0 + -1 Combine like terms: 0 + -1 = -1 4x = -1 Divide each side by '4'. x = -0.25 Simplifying x = -0.25Solution
x = {-1.25, -0.25}
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