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Simplifying 65 = 65 + -10t + -16t2 Add '-65' to each side of the equation. 65 + -65 = 65 + -10t + -65 + -16t2 Combine like terms: 65 + -65 = 0 0 = 65 + -10t + -65 + -16t2 Reorder the terms: 0 = 65 + -65 + -10t + -16t2 Combine like terms: 65 + -65 = 0 0 = 0 + -10t + -16t2 0 = -10t + -16t2 Solving 0 = -10t + -16t2 Solving for variable 't'. Remove the zero: 10t + 16t2 = -10t + -16t2 + 10t + 16t2 Reorder the terms: 10t + 16t2 = -10t + 10t + -16t2 + 16t2 Combine like terms: -10t + 10t = 0 10t + 16t2 = 0 + -16t2 + 16t2 10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 10t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2t'. 2t(5 + 8t) = 0 Ignore the factor 2.Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(5 + 8t)' equal to zero and attempt to solve: Simplifying 5 + 8t = 0 Solving 5 + 8t = 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 + 8t = 0 + -5 Combine like terms: 5 + -5 = 0 0 + 8t = 0 + -5 8t = 0 + -5 Combine like terms: 0 + -5 = -5 8t = -5 Divide each side by '8'. t = -0.625 Simplifying t = -0.625Solution
t = {0, -0.625}
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