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Simplifying (x + 4)(x + 4) = 25 Reorder the terms: (4 + x)(x + 4) = 25 Reorder the terms: (4 + x)(4 + x) = 25 Multiply (4 + x) * (4 + x) (4(4 + x) + x(4 + x)) = 25 ((4 * 4 + x * 4) + x(4 + x)) = 25 ((16 + 4x) + x(4 + x)) = 25 (16 + 4x + (4 * x + x * x)) = 25 (16 + 4x + (4x + x2)) = 25 Combine like terms: 4x + 4x = 8x (16 + 8x + x2) = 25 Solving 16 + 8x + x2 = 25 Solving for variable 'x'. Reorder the terms: 16 + -25 + 8x + x2 = 25 + -25 Combine like terms: 16 + -25 = -9 -9 + 8x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -9 + 8x + x2 = 0 Factor a trinomial. (-9 + -1x)(1 + -1x) = 0Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve: Simplifying -9 + -1x = 0 Solving -9 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -1x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1x = 0 + 9 -1x = 0 + 9 Combine like terms: 0 + 9 = 9 -1x = 9 Divide each side by '-1'. x = -9 Simplifying x = -9Subproblem 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 = {-9, 1}
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