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Simplifying 1.257 = 1.20t + 8t2 Solving 1.257 = 1.20t + 8t2 Solving for variable 't'. Reorder the terms: 1.257 + -1.20t + -8t2 = 1.20t + -1.20t + 8t2 + -8t2 Combine like terms: 1.20t + -1.20t = 0.00 1.257 + -1.20t + -8t2 = 0.00 + 8t2 + -8t2 1.257 + -1.20t + -8t2 = 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 1.257 + -1.20t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.157125 + 0.15t + t2 = 0 Move the constant term to the right: Add '0.157125' to each side of the equation. -0.157125 + 0.15t + 0.157125 + t2 = 0 + 0.157125 Reorder the terms: -0.157125 + 0.157125 + 0.15t + t2 = 0 + 0.157125 Combine like terms: -0.157125 + 0.157125 = 0.000000 0.000000 + 0.15t + t2 = 0 + 0.157125 0.15t + t2 = 0 + 0.157125 Combine like terms: 0 + 0.157125 = 0.157125 0.15t + t2 = 0.157125 The t term is 0.15t. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15t + 0.005625 + t2 = 0.157125 + 0.005625 Reorder the terms: 0.005625 + 0.15t + t2 = 0.157125 + 0.005625 Combine like terms: 0.157125 + 0.005625 = 0.16275 0.005625 + 0.15t + t2 = 0.16275 Factor a perfect square on the left side: (t + 0.075)(t + 0.075) = 0.16275 Calculate the square root of the right side: 0.403422855 Break this problem into two subproblems by setting (t + 0.075) equal to 0.403422855 and -0.403422855.Subproblem 1
t + 0.075 = 0.403422855 Simplifying t + 0.075 = 0.403422855 Reorder the terms: 0.075 + t = 0.403422855 Solving 0.075 + t = 0.403422855 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + t = 0.403422855 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + t = 0.403422855 + -0.075 t = 0.403422855 + -0.075 Combine like terms: 0.403422855 + -0.075 = 0.328422855 t = 0.328422855 Simplifying t = 0.328422855Subproblem 2
t + 0.075 = -0.403422855 Simplifying t + 0.075 = -0.403422855 Reorder the terms: 0.075 + t = -0.403422855 Solving 0.075 + t = -0.403422855 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.075' to each side of the equation. 0.075 + -0.075 + t = -0.403422855 + -0.075 Combine like terms: 0.075 + -0.075 = 0.000 0.000 + t = -0.403422855 + -0.075 t = -0.403422855 + -0.075 Combine like terms: -0.403422855 + -0.075 = -0.478422855 t = -0.478422855 Simplifying t = -0.478422855Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.328422855, -0.478422855}
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