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Simplifying (20 + 4x)(40 + 4x) = 2400 Multiply (20 + 4x) * (40 + 4x) (20(40 + 4x) + 4x * (40 + 4x)) = 2400 ((40 * 20 + 4x * 20) + 4x * (40 + 4x)) = 2400 ((800 + 80x) + 4x * (40 + 4x)) = 2400 (800 + 80x + (40 * 4x + 4x * 4x)) = 2400 (800 + 80x + (160x + 16x2)) = 2400 Combine like terms: 80x + 160x = 240x (800 + 240x + 16x2) = 2400 Solving 800 + 240x + 16x2 = 2400 Solving for variable 'x'. Reorder the terms: 800 + -2400 + 240x + 16x2 = 2400 + -2400 Combine like terms: 800 + -2400 = -1600 -1600 + 240x + 16x2 = 2400 + -2400 Combine like terms: 2400 + -2400 = 0 -1600 + 240x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-100 + 15x + x2) = 0 Factor a trinomial. 16((-20 + -1x)(5 + -1x)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-20 + -1x)' equal to zero and attempt to solve: Simplifying -20 + -1x = 0 Solving -20 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + -1x = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1x = 0 + 20 -1x = 0 + 20 Combine like terms: 0 + 20 = 20 -1x = 20 Divide each side by '-1'. x = -20 Simplifying x = -20Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve: Simplifying 5 + -1x = 0 Solving 5 + -1x = 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 + -1x = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1x = 0 + -5 -1x = 0 + -5 Combine like terms: 0 + -5 = -5 -1x = -5 Divide each side by '-1'. x = 5 Simplifying x = 5Solution
x = {-20, 5}
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