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Simplifying 4.9t2 + 3.6t + -14 = 0 Reorder the terms: -14 + 3.6t + 4.9t2 = 0 Solving -14 + 3.6t + 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'. -2.857142857 + 0.7346938776t + t2 = 0 Move the constant term to the right: Add '2.857142857' to each side of the equation. -2.857142857 + 0.7346938776t + 2.857142857 + t2 = 0 + 2.857142857 Reorder the terms: -2.857142857 + 2.857142857 + 0.7346938776t + t2 = 0 + 2.857142857 Combine like terms: -2.857142857 + 2.857142857 = 0.000000000 0.000000000 + 0.7346938776t + t2 = 0 + 2.857142857 0.7346938776t + t2 = 0 + 2.857142857 Combine like terms: 0 + 2.857142857 = 2.857142857 0.7346938776t + t2 = 2.857142857 The t term is 0.7346938776t. Take half its coefficient (0.3673469388). Square it (0.1349437734) and add it to both sides. Add '0.1349437734' to each side of the equation. 0.7346938776t + 0.1349437734 + t2 = 2.857142857 + 0.1349437734 Reorder the terms: 0.1349437734 + 0.7346938776t + t2 = 2.857142857 + 0.1349437734 Combine like terms: 2.857142857 + 0.1349437734 = 2.9920866304 0.1349437734 + 0.7346938776t + t2 = 2.9920866304 Factor a perfect square on the left side: (t + 0.3673469388)(t + 0.3673469388) = 2.9920866304 Calculate the square root of the right side: 1.729764906 Break this problem into two subproblems by setting (t + 0.3673469388) equal to 1.729764906 and -1.729764906.Subproblem 1
t + 0.3673469388 = 1.729764906 Simplifying t + 0.3673469388 = 1.729764906 Reorder the terms: 0.3673469388 + t = 1.729764906 Solving 0.3673469388 + t = 1.729764906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3673469388' to each side of the equation. 0.3673469388 + -0.3673469388 + t = 1.729764906 + -0.3673469388 Combine like terms: 0.3673469388 + -0.3673469388 = 0.0000000000 0.0000000000 + t = 1.729764906 + -0.3673469388 t = 1.729764906 + -0.3673469388 Combine like terms: 1.729764906 + -0.3673469388 = 1.3624179672 t = 1.3624179672 Simplifying t = 1.3624179672Subproblem 2
t + 0.3673469388 = -1.729764906 Simplifying t + 0.3673469388 = -1.729764906 Reorder the terms: 0.3673469388 + t = -1.729764906 Solving 0.3673469388 + t = -1.729764906 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3673469388' to each side of the equation. 0.3673469388 + -0.3673469388 + t = -1.729764906 + -0.3673469388 Combine like terms: 0.3673469388 + -0.3673469388 = 0.0000000000 0.0000000000 + t = -1.729764906 + -0.3673469388 t = -1.729764906 + -0.3673469388 Combine like terms: -1.729764906 + -0.3673469388 = -2.0971118448 t = -2.0971118448 Simplifying t = -2.0971118448Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3624179672, -2.0971118448}
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