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Simplifying -63 = -12.5t + -4.9t2 Solving -63 = -12.5t + -4.9t2 Solving for variable 't'. Reorder the terms: -63 + 12.5t + 4.9t2 = -12.5t + 12.5t + -4.9t2 + 4.9t2 Combine like terms: -12.5t + 12.5t = 0.0 -63 + 12.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -63 + 12.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -63 + 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'. -12.85714286 + 2.551020408t + t2 = 0 Move the constant term to the right: Add '12.85714286' to each side of the equation. -12.85714286 + 2.551020408t + 12.85714286 + t2 = 0 + 12.85714286 Reorder the terms: -12.85714286 + 12.85714286 + 2.551020408t + t2 = 0 + 12.85714286 Combine like terms: -12.85714286 + 12.85714286 = 0.00000000 0.00000000 + 2.551020408t + t2 = 0 + 12.85714286 2.551020408t + t2 = 0 + 12.85714286 Combine like terms: 0 + 12.85714286 = 12.85714286 2.551020408t + t2 = 12.85714286 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 = 12.85714286 + 1.626926281 Reorder the terms: 1.626926281 + 2.551020408t + t2 = 12.85714286 + 1.626926281 Combine like terms: 12.85714286 + 1.626926281 = 14.484069141 1.626926281 + 2.551020408t + t2 = 14.484069141 Factor a perfect square on the left side: (t + 1.275510204)(t + 1.275510204) = 14.484069141 Calculate the square root of the right side: 3.805794154 Break this problem into two subproblems by setting (t + 1.275510204) equal to 3.805794154 and -3.805794154.Subproblem 1
t + 1.275510204 = 3.805794154 Simplifying t + 1.275510204 = 3.805794154 Reorder the terms: 1.275510204 + t = 3.805794154 Solving 1.275510204 + t = 3.805794154 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 = 3.805794154 + -1.275510204 Combine like terms: 1.275510204 + -1.275510204 = 0.000000000 0.000000000 + t = 3.805794154 + -1.275510204 t = 3.805794154 + -1.275510204 Combine like terms: 3.805794154 + -1.275510204 = 2.53028395 t = 2.53028395 Simplifying t = 2.53028395Subproblem 2
t + 1.275510204 = -3.805794154 Simplifying t + 1.275510204 = -3.805794154 Reorder the terms: 1.275510204 + t = -3.805794154 Solving 1.275510204 + t = -3.805794154 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 = -3.805794154 + -1.275510204 Combine like terms: 1.275510204 + -1.275510204 = 0.000000000 0.000000000 + t = -3.805794154 + -1.275510204 t = -3.805794154 + -1.275510204 Combine like terms: -3.805794154 + -1.275510204 = -5.081304358 t = -5.081304358 Simplifying t = -5.081304358Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.53028395, -5.081304358}
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