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Simplifying -4.90t2 + -4.50t + 14 = 0 Reorder the terms: 14 + -4.50t + -4.90t2 = 0 Solving 14 + -4.50t + -4.90t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.90 the coefficient of the squared term: Divide each side by '-4.90'. -2.857142857 + 0.9183673469t + t2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 0.9183673469t + 2.857142857 + t2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 0.9183673469t + t2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 0.9183673469t + t2 = 0 + 2.857142857 0.9183673469t + t2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 0.9183673469t + t2 = 2.857142857 The t term is 0.9183673469t. Take half its coefficient (0.4591836735). Square it (0.2108496460) and add it to both sides. Add '0.2108496460' to each side of the equation. 0.9183673469t + 0.2108496460 + t2 = 2.857142857 + 0.2108496460 Reorder the terms: 0.2108496460 + 0.9183673469t + t2 = 2.857142857 + 0.2108496460 Combine like terms: 2.857142857 + 0.2108496460 = 3.067992503 0.2108496460 + 0.9183673469t + t2 = 3.067992503 Factor a perfect square on the left side: (t + 0.4591836735)(t + 0.4591836735) = 3.067992503 Calculate the square root of the right side: 1.751568584 Break this problem into two subproblems by setting (t + 0.4591836735) equal to 1.751568584 and -1.751568584.Subproblem 1
t + 0.4591836735 = 1.751568584 Simplifying t + 0.4591836735 = 1.751568584 Reorder the terms: 0.4591836735 + t = 1.751568584 Solving 0.4591836735 + t = 1.751568584 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4591836735' to each side of the equation. 0.4591836735 + -0.4591836735 + t = 1.751568584 + -0.4591836735 Combine like terms: 0.4591836735 + -0.4591836735 = 0.0000000000 0.0000000000 + t = 1.751568584 + -0.4591836735 t = 1.751568584 + -0.4591836735 Combine like terms: 1.751568584 + -0.4591836735 = 1.2923849105 t = 1.2923849105 Simplifying t = 1.2923849105Subproblem 2
t + 0.4591836735 = -1.751568584 Simplifying t + 0.4591836735 = -1.751568584 Reorder the terms: 0.4591836735 + t = -1.751568584 Solving 0.4591836735 + t = -1.751568584 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4591836735' to each side of the equation. 0.4591836735 + -0.4591836735 + t = -1.751568584 + -0.4591836735 Combine like terms: 0.4591836735 + -0.4591836735 = 0.0000000000 0.0000000000 + t = -1.751568584 + -0.4591836735 t = -1.751568584 + -0.4591836735 Combine like terms: -1.751568584 + -0.4591836735 = -2.2107522575 t = -2.2107522575 Simplifying t = -2.2107522575Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.2923849105, -2.2107522575}
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