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Simplifying ((x + 6)(x + 6)) + ((x)(x)) = 900 Reorder the terms: ((6 + x)(x + 6)) + ((x)(x)) = 900 Reorder the terms: ((6 + x)(6 + x)) + ((x)(x)) = 900 Multiply (6 + x) * (6 + x) ((6(6 + x) + x(6 + x))) + ((x)(x)) = 900 (((6 * 6 + x * 6) + x(6 + x))) + ((x)(x)) = 900 (((36 + 6x) + x(6 + x))) + ((x)(x)) = 900 ((36 + 6x + (6 * x + x * x))) + ((x)(x)) = 900 ((36 + 6x + (6x + x2))) + ((x)(x)) = 900 Combine like terms: 6x + 6x = 12x ((36 + 12x + x2)) + ((x)(x)) = 900 (36 + 12x + x2) + ((x)(x)) = 900 Remove parenthesis around (36 + 12x + x2) 36 + 12x + x2 + ((x)(x)) = 900 Multiply x * x 36 + 12x + x2 + (x2) = 900 36 + 12x + x2 + x2 = 900 Combine like terms: x2 + x2 = 2x2 36 + 12x + 2x2 = 900 Solving 36 + 12x + 2x2 = 900 Solving for variable 'x'. Reorder the terms: 36 + -900 + 12x + 2x2 = 900 + -900 Combine like terms: 36 + -900 = -864 -864 + 12x + 2x2 = 900 + -900 Combine like terms: 900 + -900 = 0 -864 + 12x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-432 + 6x + x2) = 0 Factor a trinomial. 2((-24 + -1x)(18 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-24 + -1x)' equal to zero and attempt to solve: Simplifying -24 + -1x = 0 Solving -24 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '24' to each side of the equation. -24 + 24 + -1x = 0 + 24 Combine like terms: -24 + 24 = 0 0 + -1x = 0 + 24 -1x = 0 + 24 Combine like terms: 0 + 24 = 24 -1x = 24 Divide each side by '-1'. x = -24 Simplifying x = -24Subproblem 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 = {-24, 18}
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