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Simplifying (x + 6)(x + 1) = 66 Reorder the terms: (6 + x)(x + 1) = 66 Reorder the terms: (6 + x)(1 + x) = 66 Multiply (6 + x) * (1 + x) (6(1 + x) + x(1 + x)) = 66 ((1 * 6 + x * 6) + x(1 + x)) = 66 ((6 + 6x) + x(1 + x)) = 66 (6 + 6x + (1 * x + x * x)) = 66 (6 + 6x + (1x + x2)) = 66 Combine like terms: 6x + 1x = 7x (6 + 7x + x2) = 66 Solving 6 + 7x + x2 = 66 Solving for variable 'x'. Reorder the terms: 6 + -66 + 7x + x2 = 66 + -66 Combine like terms: 6 + -66 = -60 -60 + 7x + x2 = 66 + -66 Combine like terms: 66 + -66 = 0 -60 + 7x + x2 = 0 Factor a trinomial. (-12 + -1x)(5 + -1x) = 0Subproblem 1
Set the factor '(-12 + -1x)' equal to zero and attempt to solve: Simplifying -12 + -1x = 0 Solving -12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1x = 0 + 12 -1x = 0 + 12 Combine like terms: 0 + 12 = 12 -1x = 12 Divide each side by '-1'. x = -12 Simplifying x = -12Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-12, 5}
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