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Simplifying 33t + -0.13t2 = 200 Solving 33t + -0.13t2 = 200 Solving for variable 't'. Reorder the terms: -200 + 33t + -0.13t2 = 200 + -200 Combine like terms: 200 + -200 = 0 -200 + 33t + -0.13t2 = 0 Begin completing the square. Divide all terms by -0.13 the coefficient of the squared term: Divide each side by '-0.13'. 1538.461538 + -253.8461538t + t2 = 0 Move the constant term to the right: Add '-1538.461538' to each side of the equation. 1538.461538 + -253.8461538t + -1538.461538 + t2 = 0 + -1538.461538 Reorder the terms: 1538.461538 + -1538.461538 + -253.8461538t + t2 = 0 + -1538.461538 Combine like terms: 1538.461538 + -1538.461538 = 0.000000 0.000000 + -253.8461538t + t2 = 0 + -1538.461538 -253.8461538t + t2 = 0 + -1538.461538 Combine like terms: 0 + -1538.461538 = -1538.461538 -253.8461538t + t2 = -1538.461538 The t term is -253.8461538t. Take half its coefficient (-126.9230769). Square it (16109.46745) and add it to both sides. Add '16109.46745' to each side of the equation. -253.8461538t + 16109.46745 + t2 = -1538.461538 + 16109.46745 Reorder the terms: 16109.46745 + -253.8461538t + t2 = -1538.461538 + 16109.46745 Combine like terms: -1538.461538 + 16109.46745 = 14571.005912 16109.46745 + -253.8461538t + t2 = 14571.005912 Factor a perfect square on the left side: (t + -126.9230769)(t + -126.9230769) = 14571.005912 Calculate the square root of the right side: 120.710421721 Break this problem into two subproblems by setting (t + -126.9230769) equal to 120.710421721 and -120.710421721.Subproblem 1
t + -126.9230769 = 120.710421721 Simplifying t + -126.9230769 = 120.710421721 Reorder the terms: -126.9230769 + t = 120.710421721 Solving -126.9230769 + t = 120.710421721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '126.9230769' to each side of the equation. -126.9230769 + 126.9230769 + t = 120.710421721 + 126.9230769 Combine like terms: -126.9230769 + 126.9230769 = 0.0000000 0.0000000 + t = 120.710421721 + 126.9230769 t = 120.710421721 + 126.9230769 Combine like terms: 120.710421721 + 126.9230769 = 247.633498621 t = 247.633498621 Simplifying t = 247.633498621Subproblem 2
t + -126.9230769 = -120.710421721 Simplifying t + -126.9230769 = -120.710421721 Reorder the terms: -126.9230769 + t = -120.710421721 Solving -126.9230769 + t = -120.710421721 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '126.9230769' to each side of the equation. -126.9230769 + 126.9230769 + t = -120.710421721 + 126.9230769 Combine like terms: -126.9230769 + 126.9230769 = 0.0000000 0.0000000 + t = -120.710421721 + 126.9230769 t = -120.710421721 + 126.9230769 Combine like terms: -120.710421721 + 126.9230769 = 6.212655179 t = 6.212655179 Simplifying t = 6.212655179Solution
The solution to the problem is based on the solutions from the subproblems. t = {247.633498621, 6.212655179}
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