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Simplifying 0 = 4x2 + 174x + 486 Reorder the terms: 0 = 486 + 174x + 4x2 Solving 0 = 486 + 174x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -486 = -486 -486 + -174x + -4x2 = 486 + 174x + 4x2 + -486 + -174x + -4x2 Reorder the terms: -486 + -174x + -4x2 = 486 + -486 + 174x + -174x + 4x2 + -4x2 Combine like terms: 486 + -486 = 0 -486 + -174x + -4x2 = 0 + 174x + -174x + 4x2 + -4x2 -486 + -174x + -4x2 = 174x + -174x + 4x2 + -4x2 Combine like terms: 174x + -174x = 0 -486 + -174x + -4x2 = 0 + 4x2 + -4x2 -486 + -174x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -486 + -174x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-2'. -2(243 + 87x + 2x2) = 0 Factor a trinomial. -2((81 + 2x)(3 + x)) = 0 Ignore the factor -2.Subproblem 1
Set the factor '(81 + 2x)' equal to zero and attempt to solve: Simplifying 81 + 2x = 0 Solving 81 + 2x = 0 Move all terms containing x to the left, all other terms to the right. Add '-81' to each side of the equation. 81 + -81 + 2x = 0 + -81 Combine like terms: 81 + -81 = 0 0 + 2x = 0 + -81 2x = 0 + -81 Combine like terms: 0 + -81 = -81 2x = -81 Divide each side by '2'. x = -40.5 Simplifying x = -40.5Subproblem 2
Set the factor '(3 + x)' equal to zero and attempt to solve: Simplifying 3 + x = 0 Solving 3 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + x = 0 + -3 x = 0 + -3 Combine like terms: 0 + -3 = -3 x = -3 Simplifying x = -3Solution
x = {-40.5, -3}
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