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Simplifying -15t2 + 60t + 10 = 55 Reorder the terms: 10 + 60t + -15t2 = 55 Solving 10 + 60t + -15t2 = 55 Solving for variable 't'. Reorder the terms: 10 + -55 + 60t + -15t2 = 55 + -55 Combine like terms: 10 + -55 = -45 -45 + 60t + -15t2 = 55 + -55 Combine like terms: 55 + -55 = 0 -45 + 60t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '15'. 15(-3 + 4t + -1t2) = 0 Factor a trinomial. 15((-3 + t)(1 + -1t)) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(-3 + t)' equal to zero and attempt to solve: Simplifying -3 + t = 0 Solving -3 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + t = 0 + 3 t = 0 + 3 Combine like terms: 0 + 3 = 3 t = 3 Simplifying t = 3Subproblem 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 = {3, 1}
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