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Simplifying 5x2 + 78x + 240 = 3x2 + 50x + 144 Reorder the terms: 240 + 78x + 5x2 = 3x2 + 50x + 144 Reorder the terms: 240 + 78x + 5x2 = 144 + 50x + 3x2 Solving 240 + 78x + 5x2 = 144 + 50x + 3x2 Solving for variable 'x'. Reorder the terms: 240 + -144 + 78x + -50x + 5x2 + -3x2 = 144 + 50x + 3x2 + -144 + -50x + -3x2 Combine like terms: 240 + -144 = 96 96 + 78x + -50x + 5x2 + -3x2 = 144 + 50x + 3x2 + -144 + -50x + -3x2 Combine like terms: 78x + -50x = 28x 96 + 28x + 5x2 + -3x2 = 144 + 50x + 3x2 + -144 + -50x + -3x2 Combine like terms: 5x2 + -3x2 = 2x2 96 + 28x + 2x2 = 144 + 50x + 3x2 + -144 + -50x + -3x2 Reorder the terms: 96 + 28x + 2x2 = 144 + -144 + 50x + -50x + 3x2 + -3x2 Combine like terms: 144 + -144 = 0 96 + 28x + 2x2 = 0 + 50x + -50x + 3x2 + -3x2 96 + 28x + 2x2 = 50x + -50x + 3x2 + -3x2 Combine like terms: 50x + -50x = 0 96 + 28x + 2x2 = 0 + 3x2 + -3x2 96 + 28x + 2x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 96 + 28x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(48 + 14x + x2) = 0 Factor a trinomial. 2((8 + x)(6 + x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8Subproblem 2
Set the factor '(6 + x)' equal to zero and attempt to solve: Simplifying 6 + x = 0 Solving 6 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 0 + -6 Combine like terms: 6 + -6 = 0 0 + x = 0 + -6 x = 0 + -6 Combine like terms: 0 + -6 = -6 x = -6 Simplifying x = -6Solution
x = {-8, -6}
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