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Simplifying 0 = -4t2 + -8t + 252 Reorder the terms: 0 = 252 + -8t + -4t2 Solving 0 = 252 + -8t + -4t2 Solving for variable 't'. Combine like terms: 0 + -252 = -252 -252 + 8t + 4t2 = 252 + -8t + -4t2 + -252 + 8t + 4t2 Reorder the terms: -252 + 8t + 4t2 = 252 + -252 + -8t + 8t + -4t2 + 4t2 Combine like terms: 252 + -252 = 0 -252 + 8t + 4t2 = 0 + -8t + 8t + -4t2 + 4t2 -252 + 8t + 4t2 = -8t + 8t + -4t2 + 4t2 Combine like terms: -8t + 8t = 0 -252 + 8t + 4t2 = 0 + -4t2 + 4t2 -252 + 8t + 4t2 = -4t2 + 4t2 Combine like terms: -4t2 + 4t2 = 0 -252 + 8t + 4t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-63 + 2t + t2) = 0 Factor a trinomial. 4((-9 + -1t)(7 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -1t)' equal to zero and attempt to solve: Simplifying -9 + -1t = 0 Solving -9 + -1t = 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 + -1t = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -1t = 0 + 9 -1t = 0 + 9 Combine like terms: 0 + 9 = 9 -1t = 9 Divide each side by '-1'. t = -9 Simplifying t = -9Subproblem 2
Set the factor '(7 + -1t)' equal to zero and attempt to solve: Simplifying 7 + -1t = 0 Solving 7 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1t = 0 + -7 -1t = 0 + -7 Combine like terms: 0 + -7 = -7 -1t = -7 Divide each side by '-1'. t = 7 Simplifying t = 7Solution
t = {-9, 7}
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