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Simplifying 256 + 144 = (12 + x)(12 + x) Combine like terms: 256 + 144 = 400 400 = (12 + x)(12 + x) Multiply (12 + x) * (12 + x) 400 = (12(12 + x) + x(12 + x)) 400 = ((12 * 12 + x * 12) + x(12 + x)) 400 = ((144 + 12x) + x(12 + x)) 400 = (144 + 12x + (12 * x + x * x)) 400 = (144 + 12x + (12x + x2)) Combine like terms: 12x + 12x = 24x 400 = (144 + 24x + x2) Solving 400 = 144 + 24x + x2 Solving for variable 'x'. Combine like terms: 400 + -144 = 256 256 + -24x + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2 Reorder the terms: 256 + -24x + -1x2 = 144 + -144 + 24x + -24x + x2 + -1x2 Combine like terms: 144 + -144 = 0 256 + -24x + -1x2 = 0 + 24x + -24x + x2 + -1x2 256 + -24x + -1x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 256 + -24x + -1x2 = 0 + x2 + -1x2 256 + -24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 256 + -24x + -1x2 = 0 Factor a trinomial. (8 + -1x)(32 + x) = 0Subproblem 1
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 = 8Subproblem 2
Set the factor '(32 + x)' equal to zero and attempt to solve: Simplifying 32 + x = 0 Solving 32 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-32' to each side of the equation. 32 + -32 + x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + x = 0 + -32 x = 0 + -32 Combine like terms: 0 + -32 = -32 x = -32 Simplifying x = -32Solution
x = {8, -32}
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