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Simplifying 16t2 + 13t + -92 = 0 Reorder the terms: -92 + 13t + 16t2 = 0 Solving -92 + 13t + 16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -5.75 + 0.8125t + t2 = 0 Move the constant term to the right: Add '5.75' to each side of the equation. -5.75 + 0.8125t + 5.75 + t2 = 0 + 5.75 Reorder the terms: -5.75 + 5.75 + 0.8125t + t2 = 0 + 5.75 Combine like terms: -5.75 + 5.75 = 0.00 0.00 + 0.8125t + t2 = 0 + 5.75 0.8125t + t2 = 0 + 5.75 Combine like terms: 0 + 5.75 = 5.75 0.8125t + t2 = 5.75 The t term is 0.8125t. Take half its coefficient (0.40625). Square it (0.1650390625) and add it to both sides. Add '0.1650390625' to each side of the equation. 0.8125t + 0.1650390625 + t2 = 5.75 + 0.1650390625 Reorder the terms: 0.1650390625 + 0.8125t + t2 = 5.75 + 0.1650390625 Combine like terms: 5.75 + 0.1650390625 = 5.9150390625 0.1650390625 + 0.8125t + t2 = 5.9150390625 Factor a perfect square on the left side: (t + 0.40625)(t + 0.40625) = 5.9150390625 Calculate the square root of the right side: 2.432085332 Break this problem into two subproblems by setting (t + 0.40625) equal to 2.432085332 and -2.432085332.Subproblem 1
t + 0.40625 = 2.432085332 Simplifying t + 0.40625 = 2.432085332 Reorder the terms: 0.40625 + t = 2.432085332 Solving 0.40625 + t = 2.432085332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + t = 2.432085332 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + t = 2.432085332 + -0.40625 t = 2.432085332 + -0.40625 Combine like terms: 2.432085332 + -0.40625 = 2.025835332 t = 2.025835332 Simplifying t = 2.025835332Subproblem 2
t + 0.40625 = -2.432085332 Simplifying t + 0.40625 = -2.432085332 Reorder the terms: 0.40625 + t = -2.432085332 Solving 0.40625 + t = -2.432085332 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.40625' to each side of the equation. 0.40625 + -0.40625 + t = -2.432085332 + -0.40625 Combine like terms: 0.40625 + -0.40625 = 0.00000 0.00000 + t = -2.432085332 + -0.40625 t = -2.432085332 + -0.40625 Combine like terms: -2.432085332 + -0.40625 = -2.838335332 t = -2.838335332 Simplifying t = -2.838335332Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.025835332, -2.838335332}
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