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Simplifying 8t2 = -15t + 9 Reorder the terms: 8t2 = 9 + -15t Solving 8t2 = 9 + -15t Solving for variable 't'. Reorder the terms: -9 + 15t + 8t2 = 9 + -15t + -9 + 15t Reorder the terms: -9 + 15t + 8t2 = 9 + -9 + -15t + 15t Combine like terms: 9 + -9 = 0 -9 + 15t + 8t2 = 0 + -15t + 15t -9 + 15t + 8t2 = -15t + 15t Combine like terms: -15t + 15t = 0 -9 + 15t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.125 + 1.875t + t2 = 0 Move the constant term to the right: Add '1.125' to each side of the equation. -1.125 + 1.875t + 1.125 + t2 = 0 + 1.125 Reorder the terms: -1.125 + 1.125 + 1.875t + t2 = 0 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + 1.875t + t2 = 0 + 1.125 1.875t + t2 = 0 + 1.125 Combine like terms: 0 + 1.125 = 1.125 1.875t + t2 = 1.125 The t term is 1.875t. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875t + 0.87890625 + t2 = 1.125 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 1.125 + 0.87890625 Combine like terms: 1.125 + 0.87890625 = 2.00390625 0.87890625 + 1.875t + t2 = 2.00390625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 2.00390625 Calculate the square root of the right side: 1.415593957 Break this problem into two subproblems by setting (t + 0.9375) equal to 1.415593957 and -1.415593957.Subproblem 1
t + 0.9375 = 1.415593957 Simplifying t + 0.9375 = 1.415593957 Reorder the terms: 0.9375 + t = 1.415593957 Solving 0.9375 + t = 1.415593957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = 1.415593957 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 1.415593957 + -0.9375 t = 1.415593957 + -0.9375 Combine like terms: 1.415593957 + -0.9375 = 0.478093957 t = 0.478093957 Simplifying t = 0.478093957Subproblem 2
t + 0.9375 = -1.415593957 Simplifying t + 0.9375 = -1.415593957 Reorder the terms: 0.9375 + t = -1.415593957 Solving 0.9375 + t = -1.415593957 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + t = -1.415593957 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -1.415593957 + -0.9375 t = -1.415593957 + -0.9375 Combine like terms: -1.415593957 + -0.9375 = -2.353093957 t = -2.353093957 Simplifying t = -2.353093957Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.478093957, -2.353093957}
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