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Simplifying 4t2 + 91t + 5 = 0 Reorder the terms: 5 + 91t + 4t2 = 0 Solving 5 + 91t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 1.25 + 22.75t + t2 = 0 Move the constant term to the right: Add '-1.25' to each side of the equation. 1.25 + 22.75t + -1.25 + t2 = 0 + -1.25 Reorder the terms: 1.25 + -1.25 + 22.75t + t2 = 0 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + 22.75t + t2 = 0 + -1.25 22.75t + t2 = 0 + -1.25 Combine like terms: 0 + -1.25 = -1.25 22.75t + t2 = -1.25 The t term is 22.75t. Take half its coefficient (11.375). Square it (129.390625) and add it to both sides. Add '129.390625' to each side of the equation. 22.75t + 129.390625 + t2 = -1.25 + 129.390625 Reorder the terms: 129.390625 + 22.75t + t2 = -1.25 + 129.390625 Combine like terms: -1.25 + 129.390625 = 128.140625 129.390625 + 22.75t + t2 = 128.140625 Factor a perfect square on the left side: (t + 11.375)(t + 11.375) = 128.140625 Calculate the square root of the right side: 11.319921599 Break this problem into two subproblems by setting (t + 11.375) equal to 11.319921599 and -11.319921599.Subproblem 1
t + 11.375 = 11.319921599 Simplifying t + 11.375 = 11.319921599 Reorder the terms: 11.375 + t = 11.319921599 Solving 11.375 + t = 11.319921599 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11.375' to each side of the equation. 11.375 + -11.375 + t = 11.319921599 + -11.375 Combine like terms: 11.375 + -11.375 = 0.000 0.000 + t = 11.319921599 + -11.375 t = 11.319921599 + -11.375 Combine like terms: 11.319921599 + -11.375 = -0.055078401 t = -0.055078401 Simplifying t = -0.055078401Subproblem 2
t + 11.375 = -11.319921599 Simplifying t + 11.375 = -11.319921599 Reorder the terms: 11.375 + t = -11.319921599 Solving 11.375 + t = -11.319921599 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-11.375' to each side of the equation. 11.375 + -11.375 + t = -11.319921599 + -11.375 Combine like terms: 11.375 + -11.375 = 0.000 0.000 + t = -11.319921599 + -11.375 t = -11.319921599 + -11.375 Combine like terms: -11.319921599 + -11.375 = -22.694921599 t = -22.694921599 Simplifying t = -22.694921599Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.055078401, -22.694921599}
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