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Simplifying 0 = -6x2 + 60x + 7200 Reorder the terms: 0 = 7200 + 60x + -6x2 Solving 0 = 7200 + 60x + -6x2 Solving for variable 'x'. Combine like terms: 0 + -7200 = -7200 -7200 + -60x + 6x2 = 7200 + 60x + -6x2 + -7200 + -60x + 6x2 Reorder the terms: -7200 + -60x + 6x2 = 7200 + -7200 + 60x + -60x + -6x2 + 6x2 Combine like terms: 7200 + -7200 = 0 -7200 + -60x + 6x2 = 0 + 60x + -60x + -6x2 + 6x2 -7200 + -60x + 6x2 = 60x + -60x + -6x2 + 6x2 Combine like terms: 60x + -60x = 0 -7200 + -60x + 6x2 = 0 + -6x2 + 6x2 -7200 + -60x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -7200 + -60x + 6x2 = 0 Factor out the Greatest Common Factor (GCF), '6'. 6(-1200 + -10x + x2) = 0 Factor a trinomial. 6((-30 + -1x)(40 + -1x)) = 0 Ignore the factor 6.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 '(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 = 40Solution
x = {-30, 40}
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