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Simplifying 0 = 4x2 + 16x + 45x + 180 Reorder the terms: 0 = 180 + 16x + 45x + 4x2 Combine like terms: 16x + 45x = 61x 0 = 180 + 61x + 4x2 Solving 0 = 180 + 61x + 4x2 Solving for variable 'x'. Combine like terms: 0 + -180 = -180 -180 + -61x + -4x2 = 180 + 61x + 4x2 + -180 + -61x + -4x2 Reorder the terms: -180 + -61x + -4x2 = 180 + -180 + 61x + -61x + 4x2 + -4x2 Combine like terms: 180 + -180 = 0 -180 + -61x + -4x2 = 0 + 61x + -61x + 4x2 + -4x2 -180 + -61x + -4x2 = 61x + -61x + 4x2 + -4x2 Combine like terms: 61x + -61x = 0 -180 + -61x + -4x2 = 0 + 4x2 + -4x2 -180 + -61x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 -180 + -61x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(180 + 61x + 4x2) = 0 Factor a trinomial. -1((45 + 4x)(4 + x)) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(45 + 4x)' equal to zero and attempt to solve: Simplifying 45 + 4x = 0 Solving 45 + 4x = 0 Move all terms containing x to the left, all other terms to the right. Add '-45' to each side of the equation. 45 + -45 + 4x = 0 + -45 Combine like terms: 45 + -45 = 0 0 + 4x = 0 + -45 4x = 0 + -45 Combine like terms: 0 + -45 = -45 4x = -45 Divide each side by '4'. x = -11.25 Simplifying x = -11.25Subproblem 2
Set the factor '(4 + x)' equal to zero and attempt to solve: Simplifying 4 + x = 0 Solving 4 + x = 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 + x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + x = 0 + -4 x = 0 + -4 Combine like terms: 0 + -4 = -4 x = -4 Simplifying x = -4Solution
x = {-11.25, -4}
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