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Simplifying 4.9t2 + 12.5t + -75 = 0 Reorder the terms: -75 + 12.5t + 4.9t2 = 0 Solving -75 + 12.5t + 4.9t2 = 0 Solving for variable 't'. 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 = 2.839468378 t = 2.839468378 Simplifying t = 2.839468378Subproblem 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 = -5.390488786 t = -5.390488786 Simplifying t = -5.390488786Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.839468378, -5.390488786}
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