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Simplifying x(x + 2) = 38(x + 4) + 8 Reorder the terms: x(2 + x) = 38(x + 4) + 8 (2 * x + x * x) = 38(x + 4) + 8 (2x + x2) = 38(x + 4) + 8 Reorder the terms: 2x + x2 = 38(4 + x) + 8 2x + x2 = (4 * 38 + x * 38) + 8 2x + x2 = (152 + 38x) + 8 Reorder the terms: 2x + x2 = 152 + 8 + 38x Combine like terms: 152 + 8 = 160 2x + x2 = 160 + 38x Solving 2x + x2 = 160 + 38x Solving for variable 'x'. Reorder the terms: -160 + 2x + -38x + x2 = 160 + 38x + -160 + -38x Combine like terms: 2x + -38x = -36x -160 + -36x + x2 = 160 + 38x + -160 + -38x Reorder the terms: -160 + -36x + x2 = 160 + -160 + 38x + -38x Combine like terms: 160 + -160 = 0 -160 + -36x + x2 = 0 + 38x + -38x -160 + -36x + x2 = 38x + -38x Combine like terms: 38x + -38x = 0 -160 + -36x + x2 = 0 Factor a trinomial. (-4 + -1x)(40 + -1x) = 0Subproblem 1
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 = -4Subproblem 2
Set the factor '(40 + -1x)' equal to zero and attempt to solve: Simplifying 40 + -1x = 0 Solving 40 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-40' to each side of the equation. 40 + -40 + -1x = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -1x = 0 + -40 -1x = 0 + -40 Combine like terms: 0 + -40 = -40 -1x = -40 Divide each side by '-1'. x = 40 Simplifying x = 40Solution
x = {-4, 40}
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