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Simplifying 1200 = (30 + -2x)(20 + -2x) Multiply (30 + -2x) * (20 + -2x) 1200 = (30(20 + -2x) + -2x * (20 + -2x)) 1200 = ((20 * 30 + -2x * 30) + -2x * (20 + -2x)) 1200 = ((600 + -60x) + -2x * (20 + -2x)) 1200 = (600 + -60x + (20 * -2x + -2x * -2x)) 1200 = (600 + -60x + (-40x + 4x2)) Combine like terms: -60x + -40x = -100x 1200 = (600 + -100x + 4x2) Solving 1200 = 600 + -100x + 4x2 Solving for variable 'x'. Combine like terms: 1200 + -600 = 600 600 + 100x + -4x2 = 600 + -100x + 4x2 + -600 + 100x + -4x2 Reorder the terms: 600 + 100x + -4x2 = 600 + -600 + -100x + 100x + 4x2 + -4x2 Combine like terms: 600 + -600 = 0 600 + 100x + -4x2 = 0 + -100x + 100x + 4x2 + -4x2 600 + 100x + -4x2 = -100x + 100x + 4x2 + -4x2 Combine like terms: -100x + 100x = 0 600 + 100x + -4x2 = 0 + 4x2 + -4x2 600 + 100x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 600 + 100x + -4x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(150 + 25x + -1x2) = 0 Factor a trinomial. 4((30 + -1x)(5 + x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(30 + -1x)' equal to zero and attempt to solve: Simplifying 30 + -1x = 0 Solving 30 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-30' to each side of the equation. 30 + -30 + -1x = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -1x = 0 + -30 -1x = 0 + -30 Combine like terms: 0 + -30 = -30 -1x = -30 Divide each side by '-1'. x = 30 Simplifying x = 30Subproblem 2
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 = -5Solution
x = {30, -5}
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