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Simplifying 16t2 + -80t + -121 = 0 Reorder the terms: -121 + -80t + 16t2 = 0 Solving -121 + -80t + 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'. -7.5625 + -5t + t2 = 0 Move the constant term to the right: Add '7.5625' to each side of the equation. -7.5625 + -5t + 7.5625 + t2 = 0 + 7.5625 Reorder the terms: -7.5625 + 7.5625 + -5t + t2 = 0 + 7.5625 Combine like terms: -7.5625 + 7.5625 = 0.0000 0.0000 + -5t + t2 = 0 + 7.5625 -5t + t2 = 0 + 7.5625 Combine like terms: 0 + 7.5625 = 7.5625 -5t + t2 = 7.5625 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 7.5625 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 7.5625 + 6.25 Combine like terms: 7.5625 + 6.25 = 13.8125 6.25 + -5t + t2 = 13.8125 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 13.8125 Calculate the square root of the right side: 3.716517187 Break this problem into two subproblems by setting (t + -2.5) equal to 3.716517187 and -3.716517187.Subproblem 1
t + -2.5 = 3.716517187 Simplifying t + -2.5 = 3.716517187 Reorder the terms: -2.5 + t = 3.716517187 Solving -2.5 + t = 3.716517187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 3.716517187 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 3.716517187 + 2.5 t = 3.716517187 + 2.5 Combine like terms: 3.716517187 + 2.5 = 6.216517187 t = 6.216517187 Simplifying t = 6.216517187Subproblem 2
t + -2.5 = -3.716517187 Simplifying t + -2.5 = -3.716517187 Reorder the terms: -2.5 + t = -3.716517187 Solving -2.5 + t = -3.716517187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -3.716517187 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -3.716517187 + 2.5 t = -3.716517187 + 2.5 Combine like terms: -3.716517187 + 2.5 = -1.216517187 t = -1.216517187 Simplifying t = -1.216517187Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.216517187, -1.216517187}
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