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Simplifying (23 + -1x)(16 + x) = 378 Multiply (23 + -1x) * (16 + x) (23(16 + x) + -1x * (16 + x)) = 378 ((16 * 23 + x * 23) + -1x * (16 + x)) = 378 ((368 + 23x) + -1x * (16 + x)) = 378 (368 + 23x + (16 * -1x + x * -1x)) = 378 (368 + 23x + (-16x + -1x2)) = 378 Combine like terms: 23x + -16x = 7x (368 + 7x + -1x2) = 378 Solving 368 + 7x + -1x2 = 378 Solving for variable 'x'. Reorder the terms: 368 + -378 + 7x + -1x2 = 378 + -378 Combine like terms: 368 + -378 = -10 -10 + 7x + -1x2 = 378 + -378 Combine like terms: 378 + -378 = 0 -10 + 7x + -1x2 = 0 Factor a trinomial. (-5 + x)(2 + -1x) = 0Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve: Simplifying -5 + x = 0 Solving -5 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 0 + 5 Combine like terms: -5 + 5 = 0 0 + x = 0 + 5 x = 0 + 5 Combine like terms: 0 + 5 = 5 x = 5 Simplifying x = 5Subproblem 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 = {5, 2}
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