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Simplifying 4.9t2 + -11.5t + -58 = 0 Reorder the terms: -58 + -11.5t + 4.9t2 = 0 Solving -58 + -11.5t + 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'. -11.83673469 + -2.346938776t + t2 = 0 Move the constant term to the right: Add '11.83673469' to each side of the equation. -11.83673469 + -2.346938776t + 11.83673469 + t2 = 0 + 11.83673469 Reorder the terms: -11.83673469 + 11.83673469 + -2.346938776t + t2 = 0 + 11.83673469 Combine like terms: -11.83673469 + 11.83673469 = 0.00000000 0.00000000 + -2.346938776t + t2 = 0 + 11.83673469 -2.346938776t + t2 = 0 + 11.83673469 Combine like terms: 0 + 11.83673469 = 11.83673469 -2.346938776t + t2 = 11.83673469 The t term is -2.346938776t. Take half its coefficient (-1.173469388). Square it (1.377030405) and add it to both sides. Add '1.377030405' to each side of the equation. -2.346938776t + 1.377030405 + t2 = 11.83673469 + 1.377030405 Reorder the terms: 1.377030405 + -2.346938776t + t2 = 11.83673469 + 1.377030405 Combine like terms: 11.83673469 + 1.377030405 = 13.213765095 1.377030405 + -2.346938776t + t2 = 13.213765095 Factor a perfect square on the left side: (t + -1.173469388)(t + -1.173469388) = 13.213765095 Calculate the square root of the right side: 3.63507429 Break this problem into two subproblems by setting (t + -1.173469388) equal to 3.63507429 and -3.63507429.Subproblem 1
t + -1.173469388 = 3.63507429 Simplifying t + -1.173469388 = 3.63507429 Reorder the terms: -1.173469388 + t = 3.63507429 Solving -1.173469388 + t = 3.63507429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.173469388' to each side of the equation. -1.173469388 + 1.173469388 + t = 3.63507429 + 1.173469388 Combine like terms: -1.173469388 + 1.173469388 = 0.000000000 0.000000000 + t = 3.63507429 + 1.173469388 t = 3.63507429 + 1.173469388 Combine like terms: 3.63507429 + 1.173469388 = 4.808543678 t = 4.808543678 Simplifying t = 4.808543678Subproblem 2
t + -1.173469388 = -3.63507429 Simplifying t + -1.173469388 = -3.63507429 Reorder the terms: -1.173469388 + t = -3.63507429 Solving -1.173469388 + t = -3.63507429 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.173469388' to each side of the equation. -1.173469388 + 1.173469388 + t = -3.63507429 + 1.173469388 Combine like terms: -1.173469388 + 1.173469388 = 0.000000000 0.000000000 + t = -3.63507429 + 1.173469388 t = -3.63507429 + 1.173469388 Combine like terms: -3.63507429 + 1.173469388 = -2.461604902 t = -2.461604902 Simplifying t = -2.461604902Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.808543678, -2.461604902}
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