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Simplifying 6 = -5(t)(t) + 10t + 1 Multiply t * t 6 = -5t2 + 10t + 1 Reorder the terms: 6 = 1 + 10t + -5t2 Solving 6 = 1 + 10t + -5t2 Solving for variable 't'. Combine like terms: 6 + -1 = 5 5 + -10t + 5t2 = 1 + 10t + -5t2 + -1 + -10t + 5t2 Reorder the terms: 5 + -10t + 5t2 = 1 + -1 + 10t + -10t + -5t2 + 5t2 Combine like terms: 1 + -1 = 0 5 + -10t + 5t2 = 0 + 10t + -10t + -5t2 + 5t2 5 + -10t + 5t2 = 10t + -10t + -5t2 + 5t2 Combine like terms: 10t + -10t = 0 5 + -10t + 5t2 = 0 + -5t2 + 5t2 5 + -10t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 5 + -10t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(1 + -2t + t2) = 0 Factor a trinomial. 5((1 + -1t)(1 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Subproblem 2
Set the factor '(1 + -1t)' equal to zero and attempt to solve: Simplifying 1 + -1t = 0 Solving 1 + -1t = 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 + -1t = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1t = 0 + -1 -1t = 0 + -1 Combine like terms: 0 + -1 = -1 -1t = -1 Divide each side by '-1'. t = 1 Simplifying t = 1Solution
t = {1, 1}
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