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Simplifying 55t = 15 + -70t2 Solving 55t = 15 + -70t2 Solving for variable 't'. Reorder the terms: -15 + 55t + 70t2 = 15 + -70t2 + -15 + 70t2 Reorder the terms: -15 + 55t + 70t2 = 15 + -15 + -70t2 + 70t2 Combine like terms: 15 + -15 = 0 -15 + 55t + 70t2 = 0 + -70t2 + 70t2 -15 + 55t + 70t2 = -70t2 + 70t2 Combine like terms: -70t2 + 70t2 = 0 -15 + 55t + 70t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + 11t + 14t2) = 0 Factor a trinomial. 5((-1 + -1t)(3 + -14t)) = 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 '(3 + -14t)' equal to zero and attempt to solve: Simplifying 3 + -14t = 0 Solving 3 + -14t = 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 + -14t = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -14t = 0 + -3 -14t = 0 + -3 Combine like terms: 0 + -3 = -3 -14t = -3 Divide each side by '-14'. t = 0.2142857143 Simplifying t = 0.2142857143Solution
t = {-1, 0.2142857143}
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