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Simplifying 3x2 + -36x + 108 + x2 = x(x + 74) + -50x Reorder the terms: 108 + -36x + 3x2 + x2 = x(x + 74) + -50x Combine like terms: 3x2 + x2 = 4x2 108 + -36x + 4x2 = x(x + 74) + -50x Reorder the terms: 108 + -36x + 4x2 = x(74 + x) + -50x 108 + -36x + 4x2 = (74 * x + x * x) + -50x 108 + -36x + 4x2 = (74x + x2) + -50x Reorder the terms: 108 + -36x + 4x2 = 74x + -50x + x2 Combine like terms: 74x + -50x = 24x 108 + -36x + 4x2 = 24x + x2 Solving 108 + -36x + 4x2 = 24x + x2 Solving for variable 'x'. Reorder the terms: 108 + -36x + -24x + 4x2 + -1x2 = 24x + x2 + -24x + -1x2 Combine like terms: -36x + -24x = -60x 108 + -60x + 4x2 + -1x2 = 24x + x2 + -24x + -1x2 Combine like terms: 4x2 + -1x2 = 3x2 108 + -60x + 3x2 = 24x + x2 + -24x + -1x2 Reorder the terms: 108 + -60x + 3x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 108 + -60x + 3x2 = 0 + x2 + -1x2 108 + -60x + 3x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 108 + -60x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(36 + -20x + x2) = 0 Factor a trinomial. 3((2 + -1x)(18 + -1x)) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(2 + -1x)' equal to zero and attempt to solve: Simplifying 2 + -1x = 0 Solving 2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1x = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x = 0 + -2 -1x = 0 + -2 Combine like terms: 0 + -2 = -2 -1x = -2 Divide each side by '-1'. x = 2 Simplifying x = 2Subproblem 2
Set the factor '(18 + -1x)' equal to zero and attempt to solve: Simplifying 18 + -1x = 0 Solving 18 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + -18 + -1x = 0 + -18 Combine like terms: 18 + -18 = 0 0 + -1x = 0 + -18 -1x = 0 + -18 Combine like terms: 0 + -18 = -18 -1x = -18 Divide each side by '-1'. x = 18 Simplifying x = 18Solution
x = {2, 18}
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