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Simplifying 30 = -16t2 + 48t + 10 Reorder the terms: 30 = 10 + 48t + -16t2 Solving 30 = 10 + 48t + -16t2 Solving for variable 't'. Combine like terms: 30 + -10 = 20 20 + -48t + 16t2 = 10 + 48t + -16t2 + -10 + -48t + 16t2 Reorder the terms: 20 + -48t + 16t2 = 10 + -10 + 48t + -48t + -16t2 + 16t2 Combine like terms: 10 + -10 = 0 20 + -48t + 16t2 = 0 + 48t + -48t + -16t2 + 16t2 20 + -48t + 16t2 = 48t + -48t + -16t2 + 16t2 Combine like terms: 48t + -48t = 0 20 + -48t + 16t2 = 0 + -16t2 + 16t2 20 + -48t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 20 + -48t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + -12t + 4t2) = 0 Factor a trinomial. 4((1 + -2t)(5 + -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 '(5 + -2t)' equal to zero and attempt to solve: Simplifying 5 + -2t = 0 Solving 5 + -2t = 0 Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -2t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2t = 0 + -5 -2t = 0 + -5 Combine like terms: 0 + -5 = -5 -2t = -5 Divide each side by '-2'. t = 2.5 Simplifying t = 2.5Solution
t = {0.5, 2.5}
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