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Simplifying 58 = 60t + -16t2 + 2 Reorder the terms: 58 = 2 + 60t + -16t2 Solving 58 = 2 + 60t + -16t2 Solving for variable 't'. Combine like terms: 58 + -2 = 56 56 + -60t + 16t2 = 2 + 60t + -16t2 + -2 + -60t + 16t2 Reorder the terms: 56 + -60t + 16t2 = 2 + -2 + 60t + -60t + -16t2 + 16t2 Combine like terms: 2 + -2 = 0 56 + -60t + 16t2 = 0 + 60t + -60t + -16t2 + 16t2 56 + -60t + 16t2 = 60t + -60t + -16t2 + 16t2 Combine like terms: 60t + -60t = 0 56 + -60t + 16t2 = 0 + -16t2 + 16t2 56 + -60t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 56 + -60t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(14 + -15t + 4t2) = 0 Factor a trinomial. 4((7 + -4t)(2 + -1t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(7 + -4t)' equal to zero and attempt to solve: Simplifying 7 + -4t = 0 Solving 7 + -4t = 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 + -4t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -4t = 0 + -7 -4t = 0 + -7 Combine like terms: 0 + -7 = -7 -4t = -7 Divide each side by '-4'. t = 1.75 Simplifying t = 1.75Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {1.75, 2}
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