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Simplifying (20 + -1x)(16 + -1x) = 192 Multiply (20 + -1x) * (16 + -1x) (20(16 + -1x) + -1x * (16 + -1x)) = 192 ((16 * 20 + -1x * 20) + -1x * (16 + -1x)) = 192 ((320 + -20x) + -1x * (16 + -1x)) = 192 (320 + -20x + (16 * -1x + -1x * -1x)) = 192 (320 + -20x + (-16x + 1x2)) = 192 Combine like terms: -20x + -16x = -36x (320 + -36x + 1x2) = 192 Solving 320 + -36x + 1x2 = 192 Solving for variable 'x'. Reorder the terms: 320 + -192 + -36x + 1x2 = 192 + -192 Combine like terms: 320 + -192 = 128 128 + -36x + 1x2 = 192 + -192 Combine like terms: 192 + -192 = 0 128 + -36x + 1x2 = 0 Factor a trinomial. (4 + -1x)(32 + -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 '(32 + -1x)' equal to zero and attempt to solve: Simplifying 32 + -1x = 0 Solving 32 + -1x = 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 + -1x = 0 + -32 Combine like terms: 32 + -32 = 0 0 + -1x = 0 + -32 -1x = 0 + -32 Combine like terms: 0 + -32 = -32 -1x = -32 Divide each side by '-1'. x = 32 Simplifying x = 32Solution
x = {4, 32}
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