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Simplifying 50 = -5t2 + -15t + 100 Reorder the terms: 50 = 100 + -15t + -5t2 Solving 50 = 100 + -15t + -5t2 Solving for variable 't'. Combine like terms: 50 + -100 = -50 -50 + 15t + 5t2 = 100 + -15t + -5t2 + -100 + 15t + 5t2 Reorder the terms: -50 + 15t + 5t2 = 100 + -100 + -15t + 15t + -5t2 + 5t2 Combine like terms: 100 + -100 = 0 -50 + 15t + 5t2 = 0 + -15t + 15t + -5t2 + 5t2 -50 + 15t + 5t2 = -15t + 15t + -5t2 + 5t2 Combine like terms: -15t + 15t = 0 -50 + 15t + 5t2 = 0 + -5t2 + 5t2 -50 + 15t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -50 + 15t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-10 + 3t + t2) = 0 Factor a trinomial. 5((-5 + -1t)(2 + -1t)) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-5 + -1t)' equal to zero and attempt to solve: Simplifying -5 + -1t = 0 Solving -5 + -1t = 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 + -1t = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1t = 0 + 5 -1t = 0 + 5 Combine like terms: 0 + 5 = 5 -1t = 5 Divide each side by '-1'. t = -5 Simplifying t = -5Subproblem 2
Set the factor '(2 + -1t)' equal to zero and attempt to solve: Simplifying 2 + -1t = 0 Solving 2 + -1t = 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 + -1t = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1t = 0 + -2 -1t = 0 + -2 Combine like terms: 0 + -2 = -2 -1t = -2 Divide each side by '-1'. t = 2 Simplifying t = 2Solution
t = {-5, 2}
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