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Simplifying 2x2 + 20x + 100 = 2500 Reorder the terms: 100 + 20x + 2x2 = 2500 Solving 100 + 20x + 2x2 = 2500 Solving for variable 'x'. Reorder the terms: 100 + -2500 + 20x + 2x2 = 2500 + -2500 Combine like terms: 100 + -2500 = -2400 -2400 + 20x + 2x2 = 2500 + -2500 Combine like terms: 2500 + -2500 = 0 -2400 + 20x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-1200 + 10x + x2) = 0 Factor a trinomial. 2((-40 + -1x)(30 + -1x)) = 0 Ignore the factor 2.Subproblem 1
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 = -40Subproblem 2
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 = 30Solution
x = {-40, 30}
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