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Simplifying 218 = -16t2 + 48t + 506 Reorder the terms: 218 = 506 + 48t + -16t2 Solving 218 = 506 + 48t + -16t2 Solving for variable 't'. Combine like terms: 218 + -506 = -288 -288 + -48t + 16t2 = 506 + 48t + -16t2 + -506 + -48t + 16t2 Reorder the terms: -288 + -48t + 16t2 = 506 + -506 + 48t + -48t + -16t2 + 16t2 Combine like terms: 506 + -506 = 0 -288 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 -288 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 -288 + -48t + 16t2 = 0 + -16t2 + 16t2 -288 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -288 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '16'. 16(-18 + -3t + t2) = 0 Factor a trinomial. 16((-3 + -1t)(6 + -1t)) = 0 Ignore the factor 16.Subproblem 1
Set the factor '(-3 + -1t)' equal to zero and attempt to solve: Simplifying -3 + -1t = 0 Solving -3 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1t = 0 + 3 -1t = 0 + 3 Combine like terms: 0 + 3 = 3 -1t = 3 Divide each side by '-1'. t = -3 Simplifying t = -3Subproblem 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 = {-3, 6}
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