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Simplifying 0 = -5t2 + 23t + 10 Reorder the terms: 0 = 10 + 23t + -5t2 Solving 0 = 10 + 23t + -5t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -23t + 5t2 = 10 + 23t + -5t2 + -10 + -23t + 5t2 Reorder the terms: -10 + -23t + 5t2 = 10 + -10 + 23t + -23t + -5t2 + 5t2 Combine like terms: 10 + -10 = 0 -10 + -23t + 5t2 = 0 + 23t + -23t + -5t2 + 5t2 -10 + -23t + 5t2 = 23t + -23t + -5t2 + 5t2 Combine like terms: 23t + -23t = 0 -10 + -23t + 5t2 = 0 + -5t2 + 5t2 -10 + -23t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -10 + -23t + 5t2 = 0 Factor a trinomial. (-2 + -5t)(5 + -1t) = 0Subproblem 1
Set the factor '(-2 + -5t)' equal to zero and attempt to solve: Simplifying -2 + -5t = 0 Solving -2 + -5t = 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 + -5t = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -5t = 0 + 2 -5t = 0 + 2 Combine like terms: 0 + 2 = 2 -5t = 2 Divide each side by '-5'. t = -0.4 Simplifying t = -0.4Subproblem 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 = {-0.4, 5}
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