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Simplifying x2 + (x + -6)(x + -6) = 90 Reorder the terms: x2 + (-6 + x)(x + -6) = 90 Reorder the terms: x2 + (-6 + x)(-6 + x) = 90 Multiply (-6 + x) * (-6 + x) x2 + (-6(-6 + x) + x(-6 + x)) = 90 x2 + ((-6 * -6 + x * -6) + x(-6 + x)) = 90 x2 + ((36 + -6x) + x(-6 + x)) = 90 x2 + (36 + -6x + (-6 * x + x * x)) = 90 x2 + (36 + -6x + (-6x + x2)) = 90 Combine like terms: -6x + -6x = -12x x2 + (36 + -12x + x2) = 90 Reorder the terms: 36 + -12x + x2 + x2 = 90 Combine like terms: x2 + x2 = 2x2 36 + -12x + 2x2 = 90 Solving 36 + -12x + 2x2 = 90 Solving for variable 'x'. Reorder the terms: 36 + -90 + -12x + 2x2 = 90 + -90 Combine like terms: 36 + -90 = -54 -54 + -12x + 2x2 = 90 + -90 Combine like terms: 90 + -90 = 0 -54 + -12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-27 + -6x + x2) = 0 Factor a trinomial. 2((-3 + -1x)(9 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -3Subproblem 2
Set the factor '(9 + -1x)' equal to zero and attempt to solve: Simplifying 9 + -1x = 0 Solving 9 + -1x = 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 + -1x = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1x = 0 + -9 -1x = 0 + -9 Combine like terms: 0 + -9 = -9 -1x = -9 Divide each side by '-1'. x = 9 Simplifying x = 9Solution
x = {-3, 9}
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