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Simplifying (8 + x)(8 + x) = 27 * 12 Multiply (8 + x) * (8 + x) (8(8 + x) + x(8 + x)) = 27 * 12 ((8 * 8 + x * 8) + x(8 + x)) = 27 * 12 ((64 + 8x) + x(8 + x)) = 27 * 12 (64 + 8x + (8 * x + x * x)) = 27 * 12 (64 + 8x + (8x + x2)) = 27 * 12 Combine like terms: 8x + 8x = 16x (64 + 16x + x2) = 27 * 12 Multiply 27 * 12 64 + 16x + x2 = 324 Solving 64 + 16x + x2 = 324 Solving for variable 'x'. Reorder the terms: 64 + -324 + 16x + x2 = 324 + -324 Combine like terms: 64 + -324 = -260 -260 + 16x + x2 = 324 + -324 Combine like terms: 324 + -324 = 0 -260 + 16x + x2 = 0 Factor a trinomial. (-26 + -1x)(10 + -1x) = 0Subproblem 1
Set the factor '(-26 + -1x)' equal to zero and attempt to solve: Simplifying -26 + -1x = 0 Solving -26 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '26' to each side of the equation. -26 + 26 + -1x = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -1x = 0 + 26 -1x = 0 + 26 Combine like terms: 0 + 26 = 26 -1x = 26 Divide each side by '-1'. x = -26 Simplifying x = -26Subproblem 2
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Solution
x = {-26, 10}
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