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Simplifying 122.5 = 14t + -0.2t2 Solving 122.5 = 14t + -0.2t2 Solving for variable 't'. Reorder the terms: 122.5 + -14t + 0.2t2 = 14t + -14t + -0.2t2 + 0.2t2 Combine like terms: 14t + -14t = 0 122.5 + -14t + 0.2t2 = 0 + -0.2t2 + 0.2t2 122.5 + -14t + 0.2t2 = -0.2t2 + 0.2t2 Combine like terms: -0.2t2 + 0.2t2 = 0.0 122.5 + -14t + 0.2t2 = 0.0 Begin completing the square. Divide all terms by 0.2 the coefficient of the squared term: Divide each side by '0.2'. 612.5 + -70t + t2 = 0 Move the constant term to the right: Add '-612.5' to each side of the equation. 612.5 + -70t + -612.5 + t2 = 0 + -612.5 Reorder the terms: 612.5 + -612.5 + -70t + t2 = 0 + -612.5 Combine like terms: 612.5 + -612.5 = 0.0 0.0 + -70t + t2 = 0 + -612.5 -70t + t2 = 0 + -612.5 Combine like terms: 0 + -612.5 = -612.5 -70t + t2 = -612.5 The t term is -70t. Take half its coefficient (-35). Square it (1225) and add it to both sides. Add '1225' to each side of the equation. -70t + 1225 + t2 = -612.5 + 1225 Reorder the terms: 1225 + -70t + t2 = -612.5 + 1225 Combine like terms: -612.5 + 1225 = 612.5 1225 + -70t + t2 = 612.5 Factor a perfect square on the left side: (t + -35)(t + -35) = 612.5 Calculate the square root of the right side: 24.748737342 Break this problem into two subproblems by setting (t + -35) equal to 24.748737342 and -24.748737342.Subproblem 1
t + -35 = 24.748737342 Simplifying t + -35 = 24.748737342 Reorder the terms: -35 + t = 24.748737342 Solving -35 + t = 24.748737342 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = 24.748737342 + 35 Combine like terms: -35 + 35 = 0 0 + t = 24.748737342 + 35 t = 24.748737342 + 35 Combine like terms: 24.748737342 + 35 = 59.748737342 t = 59.748737342 Simplifying t = 59.748737342Subproblem 2
t + -35 = -24.748737342 Simplifying t + -35 = -24.748737342 Reorder the terms: -35 + t = -24.748737342 Solving -35 + t = -24.748737342 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '35' to each side of the equation. -35 + 35 + t = -24.748737342 + 35 Combine like terms: -35 + 35 = 0 0 + t = -24.748737342 + 35 t = -24.748737342 + 35 Combine like terms: -24.748737342 + 35 = 10.251262658 t = 10.251262658 Simplifying t = 10.251262658Solution
The solution to the problem is based on the solutions from the subproblems. t = {59.748737342, 10.251262658}
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