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Simplifying 432 = -16T2 + 24T + 864 Reorder the terms: 432 = 864 + 24T + -16T2 Solving 432 = 864 + 24T + -16T2 Solving for variable 'T'. Combine like terms: 432 + -864 = -432 -432 + -24T + 16T2 = 864 + 24T + -16T2 + -864 + -24T + 16T2 Reorder the terms: -432 + -24T + 16T2 = 864 + -864 + 24T + -24T + -16T2 + 16T2 Combine like terms: 864 + -864 = 0 -432 + -24T + 16T2 = 0 + 24T + -24T + -16T2 + 16T2 -432 + -24T + 16T2 = 24T + -24T + -16T2 + 16T2 Combine like terms: 24T + -24T = 0 -432 + -24T + 16T2 = 0 + -16T2 + 16T2 -432 + -24T + 16T2 = -16T2 + 16T2 Combine like terms: -16T2 + 16T2 = 0 -432 + -24T + 16T2 = 0 Factor out the Greatest Common Factor (GCF), '8'. 8(-54 + -3T + 2T2) = 0 Factor a trinomial. 8((-9 + -2T)(6 + -1T)) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-9 + -2T)' equal to zero and attempt to solve: Simplifying -9 + -2T = 0 Solving -9 + -2T = 0 Move all terms containing T to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -2T = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -2T = 0 + 9 -2T = 0 + 9 Combine like terms: 0 + 9 = 9 -2T = 9 Divide each side by '-2'. T = -4.5 Simplifying T = -4.5Subproblem 2
Set the factor '(6 + -1T)' equal to zero and attempt to solve: Simplifying 6 + -1T = 0 Solving 6 + -1T = 0 Move all terms containing T to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -1T = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -1T = 0 + -6 -1T = 0 + -6 Combine like terms: 0 + -6 = -6 -1T = -6 Divide each side by '-1'. T = 6 Simplifying T = 6Solution
T = {-4.5, 6}
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