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Simplifying 4200 = (30)(x)(x + 4) Reorder the terms: 4200 = 30x(4 + x) 4200 = (4 * 30x + x * 30x) 4200 = (120x + 30x2) Solving 4200 = 120x + 30x2 Solving for variable 'x'. Reorder the terms: 4200 + -120x + -30x2 = 120x + -120x + 30x2 + -30x2 Combine like terms: 120x + -120x = 0 4200 + -120x + -30x2 = 0 + 30x2 + -30x2 4200 + -120x + -30x2 = 30x2 + -30x2 Combine like terms: 30x2 + -30x2 = 0 4200 + -120x + -30x2 = 0 Factor out the Greatest Common Factor (GCF), '30'. 30(140 + -4x + -1x2) = 0 Factor a trinomial. 30((10 + -1x)(14 + x)) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(10 + -1x)' equal to zero and attempt to solve: Simplifying 10 + -1x = 0 Solving 10 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1x = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1x = 0 + -10 -1x = 0 + -10 Combine like terms: 0 + -10 = -10 -1x = -10 Divide each side by '-1'. x = 10 Simplifying x = 10Subproblem 2
Set the factor '(14 + x)' equal to zero and attempt to solve: Simplifying 14 + x = 0 Solving 14 + x = 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 + x = 0 + -14 Combine like terms: 14 + -14 = 0 0 + x = 0 + -14 x = 0 + -14 Combine like terms: 0 + -14 = -14 x = -14 Simplifying x = -14Solution
x = {10, -14}
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