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Simplifying (x + 1)(x + 1) = 25 Reorder the terms: (1 + x)(x + 1) = 25 Reorder the terms: (1 + x)(1 + x) = 25 Multiply (1 + x) * (1 + x) (1(1 + x) + x(1 + x)) = 25 ((1 * 1 + x * 1) + x(1 + x)) = 25 ((1 + 1x) + x(1 + x)) = 25 (1 + 1x + (1 * x + x * x)) = 25 (1 + 1x + (1x + x2)) = 25 Combine like terms: 1x + 1x = 2x (1 + 2x + x2) = 25 Solving 1 + 2x + x2 = 25 Solving for variable 'x'. Reorder the terms: 1 + -25 + 2x + x2 = 25 + -25 Combine like terms: 1 + -25 = -24 -24 + 2x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -24 + 2x + x2 = 0 Factor a trinomial. (-6 + -1x)(4 + -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 '(4 + -1x)' equal to zero and attempt to solve: Simplifying 4 + -1x = 0 Solving 4 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -1x = 0 + -4 -1x = 0 + -4 Combine like terms: 0 + -4 = -4 -1x = -4 Divide each side by '-1'. x = 4 Simplifying x = 4Solution
x = {-6, 4}
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