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Simplifying 0 = -16x2 + 1440x + -22400 Reorder the terms: 0 = -22400 + 1440x + -16x2 Solving 0 = -22400 + 1440x + -16x2 Solving for variable 'x'. Combine like terms: 0 + 22400 = 22400 22400 + -1440x + 16x2 = -22400 + 1440x + -16x2 + 22400 + -1440x + 16x2 Reorder the terms: 22400 + -1440x + 16x2 = -22400 + 22400 + 1440x + -1440x + -16x2 + 16x2 Combine like terms: -22400 + 22400 = 0 22400 + -1440x + 16x2 = 0 + 1440x + -1440x + -16x2 + 16x2 22400 + -1440x + 16x2 = 1440x + -1440x + -16x2 + 16x2 Combine like terms: 1440x + -1440x = 0 22400 + -1440x + 16x2 = 0 + -16x2 + 16x2 22400 + -1440x + 16x2 = -16x2 + 16x2 Combine like terms: -16x2 + 16x2 = 0 22400 + -1440x + 16x2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(1400 + -90x + x2) = 0 Factor a trinomial. 16((20 + -1x)(70 + -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 '(70 + -1x)' equal to zero and attempt to solve: Simplifying 70 + -1x = 0 Solving 70 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-70' to each side of the equation. 70 + -70 + -1x = 0 + -70 Combine like terms: 70 + -70 = 0 0 + -1x = 0 + -70 -1x = 0 + -70 Combine like terms: 0 + -70 = -70 -1x = -70 Divide each side by '-1'. x = 70 Simplifying x = 70Solution
x = {20, 70}
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