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Simplifying 0 = 75 + 12.5t + -4.9t2 Solving 0 = 75 + 12.5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -75 = -75 -75 + -12.5t + 4.9t2 = 75 + 12.5t + -4.9t2 + -75 + -12.5t + 4.9t2 Reorder the terms: -75 + -12.5t + 4.9t2 = 75 + -75 + 12.5t + -12.5t + -4.9t2 + 4.9t2 Combine like terms: 75 + -75 = 0 -75 + -12.5t + 4.9t2 = 0 + 12.5t + -12.5t + -4.9t2 + 4.9t2 -75 + -12.5t + 4.9t2 = 12.5t + -12.5t + -4.9t2 + 4.9t2 Combine like terms: 12.5t + -12.5t = 0.0 -75 + -12.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -75 + -12.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -75 + -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'. -15.30612245 + -2.551020408t + t2 = 0 Move the constant term to the right: Add '15.30612245' to each side of the equation. -15.30612245 + -2.551020408t + 15.30612245 + t2 = 0 + 15.30612245 Reorder the terms: -15.30612245 + 15.30612245 + -2.551020408t + t2 = 0 + 15.30612245 Combine like terms: -15.30612245 + 15.30612245 = 0.00000000 0.00000000 + -2.551020408t + t2 = 0 + 15.30612245 -2.551020408t + t2 = 0 + 15.30612245 Combine like terms: 0 + 15.30612245 = 15.30612245 -2.551020408t + t2 = 15.30612245 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 = 15.30612245 + 1.626926281 Reorder the terms: 1.626926281 + -2.551020408t + t2 = 15.30612245 + 1.626926281 Combine like terms: 15.30612245 + 1.626926281 = 16.933048731 1.626926281 + -2.551020408t + t2 = 16.933048731 Factor a perfect square on the left side: (t + -1.275510204)(t + -1.275510204) = 16.933048731 Calculate the square root of the right side: 4.114978582 Break this problem into two subproblems by setting (t + -1.275510204) equal to 4.114978582 and -4.114978582.Subproblem 1
t + -1.275510204 = 4.114978582 Simplifying t + -1.275510204 = 4.114978582 Reorder the terms: -1.275510204 + t = 4.114978582 Solving -1.275510204 + t = 4.114978582 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 = 4.114978582 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + t = 4.114978582 + 1.275510204 t = 4.114978582 + 1.275510204 Combine like terms: 4.114978582 + 1.275510204 = 5.390488786 t = 5.390488786 Simplifying t = 5.390488786Subproblem 2
t + -1.275510204 = -4.114978582 Simplifying t + -1.275510204 = -4.114978582 Reorder the terms: -1.275510204 + t = -4.114978582 Solving -1.275510204 + t = -4.114978582 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 = -4.114978582 + 1.275510204 Combine like terms: -1.275510204 + 1.275510204 = 0.000000000 0.000000000 + t = -4.114978582 + 1.275510204 t = -4.114978582 + 1.275510204 Combine like terms: -4.114978582 + 1.275510204 = -2.839468378 t = -2.839468378 Simplifying t = -2.839468378Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.390488786, -2.839468378}
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