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Simplifying (x + 5)(x + 5) = 12x + 73 Reorder the terms: (5 + x)(x + 5) = 12x + 73 Reorder the terms: (5 + x)(5 + x) = 12x + 73 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 12x + 73 ((5 * 5 + x * 5) + x(5 + x)) = 12x + 73 ((25 + 5x) + x(5 + x)) = 12x + 73 (25 + 5x + (5 * x + x * x)) = 12x + 73 (25 + 5x + (5x + x2)) = 12x + 73 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 12x + 73 Reorder the terms: 25 + 10x + x2 = 73 + 12x Solving 25 + 10x + x2 = 73 + 12x Solving for variable 'x'. Reorder the terms: 25 + -73 + 10x + -12x + x2 = 73 + 12x + -73 + -12x Combine like terms: 25 + -73 = -48 -48 + 10x + -12x + x2 = 73 + 12x + -73 + -12x Combine like terms: 10x + -12x = -2x -48 + -2x + x2 = 73 + 12x + -73 + -12x Reorder the terms: -48 + -2x + x2 = 73 + -73 + 12x + -12x Combine like terms: 73 + -73 = 0 -48 + -2x + x2 = 0 + 12x + -12x -48 + -2x + x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -48 + -2x + x2 = 0 Factor a trinomial. (-6 + -1x)(8 + -1x) = 0Subproblem 1
Set the factor '(-6 + -1x)' equal to zero and attempt to solve: Simplifying -6 + -1x = 0 Solving -6 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + -1x = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1x = 0 + 6 -1x = 0 + 6 Combine like terms: 0 + 6 = 6 -1x = 6 Divide each side by '-1'. x = -6 Simplifying x = -6Subproblem 2
Set the factor '(8 + -1x)' equal to zero and attempt to solve: Simplifying 8 + -1x = 0 Solving 8 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1x = 0 + -8 -1x = 0 + -8 Combine like terms: 0 + -8 = -8 -1x = -8 Divide each side by '-1'. x = 8 Simplifying x = 8Solution
x = {-6, 8}
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