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Simplifying 2x(x + 1) = 420 Reorder the terms: 2x(1 + x) = 420 (1 * 2x + x * 2x) = 420 (2x + 2x2) = 420 Solving 2x + 2x2 = 420 Solving for variable 'x'. Reorder the terms: -420 + 2x + 2x2 = 420 + -420 Combine like terms: 420 + -420 = 0 -420 + 2x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-210 + x + x2) = 0 Factor a trinomial. 2((-15 + -1x)(14 + -1x)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-15 + -1x)' equal to zero and attempt to solve: Simplifying -15 + -1x = 0 Solving -15 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + -1x = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -1x = 0 + 15 -1x = 0 + 15 Combine like terms: 0 + 15 = 15 -1x = 15 Divide each side by '-1'. x = -15 Simplifying x = -15Subproblem 2
Set the factor '(14 + -1x)' equal to zero and attempt to solve: Simplifying 14 + -1x = 0 Solving 14 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + -1x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -1x = 0 + -14 -1x = 0 + -14 Combine like terms: 0 + -14 = -14 -1x = -14 Divide each side by '-1'. x = 14 Simplifying x = 14Solution
x = {-15, 14}
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