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Simplifying 24 = (6 + -1X)(8 + -1X) Multiply (6 + -1X) * (8 + -1X) 24 = (6(8 + -1X) + -1X * (8 + -1X)) 24 = ((8 * 6 + -1X * 6) + -1X * (8 + -1X)) 24 = ((48 + -6X) + -1X * (8 + -1X)) 24 = (48 + -6X + (8 * -1X + -1X * -1X)) 24 = (48 + -6X + (-8X + 1X2)) Combine like terms: -6X + -8X = -14X 24 = (48 + -14X + 1X2) Solving 24 = 48 + -14X + 1X2 Solving for variable 'X'. Combine like terms: 24 + -48 = -24 -24 + 14X + -1X2 = 48 + -14X + 1X2 + -48 + 14X + -1X2 Reorder the terms: -24 + 14X + -1X2 = 48 + -48 + -14X + 14X + 1X2 + -1X2 Combine like terms: 48 + -48 = 0 -24 + 14X + -1X2 = 0 + -14X + 14X + 1X2 + -1X2 -24 + 14X + -1X2 = -14X + 14X + 1X2 + -1X2 Combine like terms: -14X + 14X = 0 -24 + 14X + -1X2 = 0 + 1X2 + -1X2 -24 + 14X + -1X2 = 1X2 + -1X2 Combine like terms: 1X2 + -1X2 = 0 -24 + 14X + -1X2 = 0 Factor a trinomial. (-12 + X)(2 + -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 '(2 + -1X)' equal to zero and attempt to solve: Simplifying 2 + -1X = 0 Solving 2 + -1X = 0 Move all terms containing X to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1X = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1X = 0 + -2 -1X = 0 + -2 Combine like terms: 0 + -2 = -2 -1X = -2 Divide each side by '-1'. X = 2 Simplifying X = 2Solution
X = {12, 2}
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