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Simplifying x(2x + 2) + x(2x + 4) = 4x + 72 Reorder the terms: x(2 + 2x) + x(2x + 4) = 4x + 72 (2 * x + 2x * x) + x(2x + 4) = 4x + 72 (2x + 2x2) + x(2x + 4) = 4x + 72 Reorder the terms: 2x + 2x2 + x(4 + 2x) = 4x + 72 2x + 2x2 + (4 * x + 2x * x) = 4x + 72 2x + 2x2 + (4x + 2x2) = 4x + 72 Reorder the terms: 2x + 4x + 2x2 + 2x2 = 4x + 72 Combine like terms: 2x + 4x = 6x 6x + 2x2 + 2x2 = 4x + 72 Combine like terms: 2x2 + 2x2 = 4x2 6x + 4x2 = 4x + 72 Reorder the terms: 6x + 4x2 = 72 + 4x Solving 6x + 4x2 = 72 + 4x Solving for variable 'x'. Reorder the terms: -72 + 6x + -4x + 4x2 = 72 + 4x + -72 + -4x Combine like terms: 6x + -4x = 2x -72 + 2x + 4x2 = 72 + 4x + -72 + -4x Reorder the terms: -72 + 2x + 4x2 = 72 + -72 + 4x + -4x Combine like terms: 72 + -72 = 0 -72 + 2x + 4x2 = 0 + 4x + -4x -72 + 2x + 4x2 = 4x + -4x Combine like terms: 4x + -4x = 0 -72 + 2x + 4x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-36 + x + 2x2) = 0 Factor a trinomial. 2((-9 + -2x)(4 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + -2x)' equal to zero and attempt to solve: Simplifying -9 + -2x = 0 Solving -9 + -2x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2x = 0 + 9 -2x = 0 + 9 Combine like terms: 0 + 9 = 9 -2x = 9 Divide each side by '-2'. x = -4.5 Simplifying x = -4.5Subproblem 2
Set the factor '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 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 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-4.5, 4}
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