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Simplifying 32 = -16t2 + 64t + 4 Reorder the terms: 32 = 4 + 64t + -16t2 Solving 32 = 4 + 64t + -16t2 Solving for variable 't'. Combine like terms: 32 + -4 = 28 28 + -64t + 16t2 = 4 + 64t + -16t2 + -4 + -64t + 16t2 Reorder the terms: 28 + -64t + 16t2 = 4 + -4 + 64t + -64t + -16t2 + 16t2 Combine like terms: 4 + -4 = 0 28 + -64t + 16t2 = 0 + 64t + -64t + -16t2 + 16t2 28 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 28 + -64t + 16t2 = 0 + -16t2 + 16t2 28 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 28 + -64t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(7 + -16t + 4t2) = 0 Factor a trinomial. 4((1 + -2t)(7 + -2t)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(1 + -2t)' equal to zero and attempt to solve: Simplifying 1 + -2t = 0 Solving 1 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -2t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2t = 0 + -1 -2t = 0 + -1 Combine like terms: 0 + -1 = -1 -2t = -1 Divide each side by '-2'. t = 0.5 Simplifying t = 0.5Subproblem 2
Set the factor '(7 + -2t)' equal to zero and attempt to solve: Simplifying 7 + -2t = 0 Solving 7 + -2t = 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 + -2t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -2t = 0 + -7 -2t = 0 + -7 Combine like terms: 0 + -7 = -7 -2t = -7 Divide each side by '-2'. t = 3.5 Simplifying t = 3.5Solution
t = {0.5, 3.5}
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