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Simplifying 0 = 8t2 + 15t + -7 Reorder the terms: 0 = -7 + 15t + 8t2 Solving 0 = -7 + 15t + 8t2 Solving for variable 't'. Combine like terms: 0 + 7 = 7 7 + -15t + -8t2 = -7 + 15t + 8t2 + 7 + -15t + -8t2 Reorder the terms: 7 + -15t + -8t2 = -7 + 7 + 15t + -15t + 8t2 + -8t2 Combine like terms: -7 + 7 = 0 7 + -15t + -8t2 = 0 + 15t + -15t + 8t2 + -8t2 7 + -15t + -8t2 = 15t + -15t + 8t2 + -8t2 Combine like terms: 15t + -15t = 0 7 + -15t + -8t2 = 0 + 8t2 + -8t2 7 + -15t + -8t2 = 8t2 + -8t2 Combine like terms: 8t2 + -8t2 = 0 7 + -15t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.875 + 1.875t + t2 = 0 Move the constant term to the right: Add '0.875' to each side of the equation. -0.875 + 1.875t + 0.875 + t2 = 0 + 0.875 Reorder the terms: -0.875 + 0.875 + 1.875t + t2 = 0 + 0.875 Combine like terms: -0.875 + 0.875 = 0.000 0.000 + 1.875t + t2 = 0 + 0.875 1.875t + t2 = 0 + 0.875 Combine like terms: 0 + 0.875 = 0.875 1.875t + t2 = 0.875 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 = 0.875 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 0.875 + 0.87890625 Combine like terms: 0.875 + 0.87890625 = 1.75390625 0.87890625 + 1.875t + t2 = 1.75390625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 1.75390625 Calculate the square root of the right side: 1.324351256 Break this problem into two subproblems by setting (t + 0.9375) equal to 1.324351256 and -1.324351256.Subproblem 1
t + 0.9375 = 1.324351256 Simplifying t + 0.9375 = 1.324351256 Reorder the terms: 0.9375 + t = 1.324351256 Solving 0.9375 + t = 1.324351256 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 = 1.324351256 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 1.324351256 + -0.9375 t = 1.324351256 + -0.9375 Combine like terms: 1.324351256 + -0.9375 = 0.386851256 t = 0.386851256 Simplifying t = 0.386851256Subproblem 2
t + 0.9375 = -1.324351256 Simplifying t + 0.9375 = -1.324351256 Reorder the terms: 0.9375 + t = -1.324351256 Solving 0.9375 + t = -1.324351256 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 = -1.324351256 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -1.324351256 + -0.9375 t = -1.324351256 + -0.9375 Combine like terms: -1.324351256 + -0.9375 = -2.261851256 t = -2.261851256 Simplifying t = -2.261851256Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.386851256, -2.261851256}
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