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Simplifying (20 + -1x)(23 + -1x) = 340 Multiply (20 + -1x) * (23 + -1x) (20(23 + -1x) + -1x * (23 + -1x)) = 340 ((23 * 20 + -1x * 20) + -1x * (23 + -1x)) = 340 ((460 + -20x) + -1x * (23 + -1x)) = 340 (460 + -20x + (23 * -1x + -1x * -1x)) = 340 (460 + -20x + (-23x + 1x2)) = 340 Combine like terms: -20x + -23x = -43x (460 + -43x + 1x2) = 340 Solving 460 + -43x + 1x2 = 340 Solving for variable 'x'. Reorder the terms: 460 + -340 + -43x + 1x2 = 340 + -340 Combine like terms: 460 + -340 = 120 120 + -43x + 1x2 = 340 + -340 Combine like terms: 340 + -340 = 0 120 + -43x + 1x2 = 0 Factor a trinomial. (3 + -1x)(40 + -1x) = 0Subproblem 1
Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3Subproblem 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 = {3, 40}
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