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Simplifying (x + 5)(x + 5) = 36 Reorder the terms: (5 + x)(x + 5) = 36 Reorder the terms: (5 + x)(5 + x) = 36 Multiply (5 + x) * (5 + x) (5(5 + x) + x(5 + x)) = 36 ((5 * 5 + x * 5) + x(5 + x)) = 36 ((25 + 5x) + x(5 + x)) = 36 (25 + 5x + (5 * x + x * x)) = 36 (25 + 5x + (5x + x2)) = 36 Combine like terms: 5x + 5x = 10x (25 + 10x + x2) = 36 Solving 25 + 10x + x2 = 36 Solving for variable 'x'. Reorder the terms: 25 + -36 + 10x + x2 = 36 + -36 Combine like terms: 25 + -36 = -11 -11 + 10x + x2 = 36 + -36 Combine like terms: 36 + -36 = 0 -11 + 10x + x2 = 0 Factor a trinomial. (-11 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-11 + -1x)' equal to zero and attempt to solve: Simplifying -11 + -1x = 0 Solving -11 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1x = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1x = 0 + 11 -1x = 0 + 11 Combine like terms: 0 + 11 = 11 -1x = 11 Divide each side by '-1'. x = -11 Simplifying x = -11Subproblem 2
Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1Solution
x = {-11, 1}
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