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Simplifying 65 = 65 + -10t + -5t2 Add '-65' to each side of the equation. 65 + -65 = 65 + -10t + -65 + -5t2 Combine like terms: 65 + -65 = 0 0 = 65 + -10t + -65 + -5t2 Reorder the terms: 0 = 65 + -65 + -10t + -5t2 Combine like terms: 65 + -65 = 0 0 = 0 + -10t + -5t2 0 = -10t + -5t2 Solving 0 = -10t + -5t2 Solving for variable 't'. Remove the zero: 10t + 5t2 = -10t + -5t2 + 10t + 5t2 Reorder the terms: 10t + 5t2 = -10t + 10t + -5t2 + 5t2 Combine like terms: -10t + 10t = 0 10t + 5t2 = 0 + -5t2 + 5t2 10t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 10t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5t'. 5t(2 + t) = 0 Ignore the factor 5.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 '(2 + t)' equal to zero and attempt to solve: Simplifying 2 + t = 0 Solving 2 + t = 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 + t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + t = 0 + -2 t = 0 + -2 Combine like terms: 0 + -2 = -2 t = -2 Simplifying t = -2Solution
t = {0, -2}
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