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Simplifying 0 = -5t2 + 22t + 15 Reorder the terms: 0 = 15 + 22t + -5t2 Solving 0 = 15 + 22t + -5t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -22t + 5t2 = 15 + 22t + -5t2 + -15 + -22t + 5t2 Reorder the terms: -15 + -22t + 5t2 = 15 + -15 + 22t + -22t + -5t2 + 5t2 Combine like terms: 15 + -15 = 0 -15 + -22t + 5t2 = 0 + 22t + -22t + -5t2 + 5t2 -15 + -22t + 5t2 = 22t + -22t + -5t2 + 5t2 Combine like terms: 22t + -22t = 0 -15 + -22t + 5t2 = 0 + -5t2 + 5t2 -15 + -22t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -15 + -22t + 5t2 = 0 Factor a trinomial. (-3 + -5t)(5 + -1t) = 0Subproblem 1
Set the factor '(-3 + -5t)' equal to zero and attempt to solve: Simplifying -3 + -5t = 0 Solving -3 + -5t = 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 + -5t = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5t = 0 + 3 -5t = 0 + 3 Combine like terms: 0 + 3 = 3 -5t = 3 Divide each side by '-5'. t = -0.6 Simplifying t = -0.6Subproblem 2
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 = 5Solution
t = {-0.6, 5}
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