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Simplifying -21 = -12.5t + -4.9t2 Solving -21 = -12.5t + -4.9t2 Solving for variable 't'. Reorder the terms: -21 + 12.5t + 4.9t2 = -12.5t + 12.5t + -4.9t2 + 4.9t2 Combine like terms: -12.5t + 12.5t = 0.0 -21 + 12.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -21 + 12.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -21 + 12.5t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -4.285714286 + 2.551020408t + t2 = 0 Move the constant term to the right: Add '4.285714286' to each side of the equation. -4.285714286 + 2.551020408t + 4.285714286 + t2 = 0 + 4.285714286 Reorder the terms: -4.285714286 + 4.285714286 + 2.551020408t + t2 = 0 + 4.285714286 Combine like terms: -4.285714286 + 4.285714286 = 0.000000000 0.000000000 + 2.551020408t + t2 = 0 + 4.285714286 2.551020408t + t2 = 0 + 4.285714286 Combine like terms: 0 + 4.285714286 = 4.285714286 2.551020408t + t2 = 4.285714286 The t term is 2.551020408t. Take half its coefficient (1.275510204). Square it (1.626926281) and add it to both sides. Add '1.626926281' to each side of the equation. 2.551020408t + 1.626926281 + t2 = 4.285714286 + 1.626926281 Reorder the terms: 1.626926281 + 2.551020408t + t2 = 4.285714286 + 1.626926281 Combine like terms: 4.285714286 + 1.626926281 = 5.912640567 1.626926281 + 2.551020408t + t2 = 5.912640567 Factor a perfect square on the left side: (t + 1.275510204)(t + 1.275510204) = 5.912640567 Calculate the square root of the right side: 2.431592188 Break this problem into two subproblems by setting (t + 1.275510204) equal to 2.431592188 and -2.431592188.Subproblem 1
t + 1.275510204 = 2.431592188 Simplifying t + 1.275510204 = 2.431592188 Reorder the terms: 1.275510204 + t = 2.431592188 Solving 1.275510204 + t = 2.431592188 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.275510204' to each side of the equation. 1.275510204 + -1.275510204 + t = 2.431592188 + -1.275510204 Combine like terms: 1.275510204 + -1.275510204 = 0.000000000 0.000000000 + t = 2.431592188 + -1.275510204 t = 2.431592188 + -1.275510204 Combine like terms: 2.431592188 + -1.275510204 = 1.156081984 t = 1.156081984 Simplifying t = 1.156081984Subproblem 2
t + 1.275510204 = -2.431592188 Simplifying t + 1.275510204 = -2.431592188 Reorder the terms: 1.275510204 + t = -2.431592188 Solving 1.275510204 + t = -2.431592188 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.275510204' to each side of the equation. 1.275510204 + -1.275510204 + t = -2.431592188 + -1.275510204 Combine like terms: 1.275510204 + -1.275510204 = 0.000000000 0.000000000 + t = -2.431592188 + -1.275510204 t = -2.431592188 + -1.275510204 Combine like terms: -2.431592188 + -1.275510204 = -3.707102392 t = -3.707102392 Simplifying t = -3.707102392Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.156081984, -3.707102392}
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