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Simplifying (x2 + -4) + (x2 + 30x + -14) = 90 Reorder the terms: (-4 + x2) + (x2 + 30x + -14) = 90 Remove parenthesis around (-4 + x2) -4 + x2 + (x2 + 30x + -14) = 90 Reorder the terms: -4 + x2 + (-14 + 30x + x2) = 90 Remove parenthesis around (-14 + 30x + x2) -4 + x2 + -14 + 30x + x2 = 90 Reorder the terms: -4 + -14 + 30x + x2 + x2 = 90 Combine like terms: -4 + -14 = -18 -18 + 30x + x2 + x2 = 90 Combine like terms: x2 + x2 = 2x2 -18 + 30x + 2x2 = 90 Solving -18 + 30x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: -18 + -90 + 30x + 2x2 = 90 + -90 Combine like terms: -18 + -90 = -108 -108 + 30x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -108 + 30x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-54 + 15x + x2) = 0 Factor a trinomial. 2((-18 + -1x)(3 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -18Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 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 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Solution
x = {-18, 3}
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