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Simplifying 100 = (20t) + 0.5(-2t2) Remove parenthesis around (-2t2) 100 = (20t) + 0.5 * -2t2 Multiply 0.5 * -2 100 = (20t) + -1t2 Solving 100 = (20t) + -1t2 Solving for variable 't'. Reorder the terms: 100 + (-20t) + t2 = (20t) + (-20t) + -1t2 + t2 Combine like terms: (20t) + (-20t) = 0 100 + (-20t) + t2 = 0 + -1t2 + t2 100 + (-20t) + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 100 + (-20t) + t2 = 0 Factor a trinomial. (10 + -1t)(10 + -1t) = 0Subproblem 1
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Subproblem 2
Set the factor '(10 + -1t)' equal to zero and attempt to solve: Simplifying 10 + -1t = 0 Solving 10 + -1t = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + -1t = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -1t = 0 + -10 -1t = 0 + -10 Combine like terms: 0 + -10 = -10 -1t = -10 Divide each side by '-1'. t = 10 Simplifying t = 10Solution
t = {10, 10}
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