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Simplifying 48x = (x + 12)(x + 12) Reorder the terms: 48x = (12 + x)(x + 12) Reorder the terms: 48x = (12 + x)(12 + x) Multiply (12 + x) * (12 + x) 48x = (12(12 + x) + x(12 + x)) 48x = ((12 * 12 + x * 12) + x(12 + x)) 48x = ((144 + 12x) + x(12 + x)) 48x = (144 + 12x + (12 * x + x * x)) 48x = (144 + 12x + (12x + x2)) Combine like terms: 12x + 12x = 24x 48x = (144 + 24x + x2) Solving 48x = 144 + 24x + x2 Solving for variable 'x'. Reorder the terms: -144 + 48x + -24x + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2 Combine like terms: 48x + -24x = 24x -144 + 24x + -1x2 = 144 + 24x + x2 + -144 + -24x + -1x2 Reorder the terms: -144 + 24x + -1x2 = 144 + -144 + 24x + -24x + x2 + -1x2 Combine like terms: 144 + -144 = 0 -144 + 24x + -1x2 = 0 + 24x + -24x + x2 + -1x2 -144 + 24x + -1x2 = 24x + -24x + x2 + -1x2 Combine like terms: 24x + -24x = 0 -144 + 24x + -1x2 = 0 + x2 + -1x2 -144 + 24x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -144 + 24x + -1x2 = 0 Factor a trinomial. (-12 + x)(12 + -1x) = 0Subproblem 1
Set the factor '(-12 + x)' equal to zero and attempt to solve: Simplifying -12 + x = 0 Solving -12 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 0 + 12 Combine like terms: -12 + 12 = 0 0 + x = 0 + 12 x = 0 + 12 Combine like terms: 0 + 12 = 12 x = 12 Simplifying x = 12Subproblem 2
Set the factor '(12 + -1x)' equal to zero and attempt to solve: Simplifying 12 + -1x = 0 Solving 12 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + -1x = 0 + -12 Combine like terms: 12 + -12 = 0 0 + -1x = 0 + -12 -1x = 0 + -12 Combine like terms: 0 + -12 = -12 -1x = -12 Divide each side by '-1'. x = 12 Simplifying x = 12Solution
x = {12, 12}
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