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Simplifying 14 = 5t + 0.5 * 2t2 Multiply 0.5 * 2 14 = 5t + 1t2 Solving 14 = 5t + 1t2 Solving for variable 't'. Reorder the terms: 14 + -5t + -1t2 = 5t + -5t + 1t2 + -1t2 Combine like terms: 5t + -5t = 0 14 + -5t + -1t2 = 0 + 1t2 + -1t2 14 + -5t + -1t2 = 1t2 + -1t2 Combine like terms: 1t2 + -1t2 = 0 14 + -5t + -1t2 = 0 Factor a trinomial. (2 + -1t)(7 + t) = 0Subproblem 1
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 = 2Subproblem 2
Set the factor '(7 + t)' equal to zero and attempt to solve: Simplifying 7 + t = 0 Solving 7 + t = 0 Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + t = 0 + -7 Combine like terms: 7 + -7 = 0 0 + t = 0 + -7 t = 0 + -7 Combine like terms: 0 + -7 = -7 t = -7 Simplifying t = -7Solution
t = {2, -7}
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