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Simplifying 0 = (40 + -1x)(50 + -2x) Multiply (40 + -1x) * (50 + -2x) 0 = (40(50 + -2x) + -1x * (50 + -2x)) 0 = ((50 * 40 + -2x * 40) + -1x * (50 + -2x)) 0 = ((2000 + -80x) + -1x * (50 + -2x)) 0 = (2000 + -80x + (50 * -1x + -2x * -1x)) 0 = (2000 + -80x + (-50x + 2x2)) Combine like terms: -80x + -50x = -130x 0 = (2000 + -130x + 2x2) Solving 0 = 2000 + -130x + 2x2 Solving for variable 'x'. Combine like terms: 0 + -2000 = -2000 -2000 + 130x + -2x2 = 2000 + -130x + 2x2 + -2000 + 130x + -2x2 Reorder the terms: -2000 + 130x + -2x2 = 2000 + -2000 + -130x + 130x + 2x2 + -2x2 Combine like terms: 2000 + -2000 = 0 -2000 + 130x + -2x2 = 0 + -130x + 130x + 2x2 + -2x2 -2000 + 130x + -2x2 = -130x + 130x + 2x2 + -2x2 Combine like terms: -130x + 130x = 0 -2000 + 130x + -2x2 = 0 + 2x2 + -2x2 -2000 + 130x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -2000 + 130x + -2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1000 + 65x + -1x2) = 0 Factor a trinomial. 2((-40 + x)(25 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-40 + x)' equal to zero and attempt to solve: Simplifying -40 + x = 0 Solving -40 + x = 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 + x = 0 + 40 Combine like terms: -40 + 40 = 0 0 + x = 0 + 40 x = 0 + 40 Combine like terms: 0 + 40 = 40 x = 40 Simplifying x = 40Subproblem 2
Set the factor '(25 + -1x)' equal to zero and attempt to solve: Simplifying 25 + -1x = 0 Solving 25 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-25' to each side of the equation. 25 + -25 + -1x = 0 + -25 Combine like terms: 25 + -25 = 0 0 + -1x = 0 + -25 -1x = 0 + -25 Combine like terms: 0 + -25 = -25 -1x = -25 Divide each side by '-1'. x = 25 Simplifying x = 25Solution
x = {40, 25}
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