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Simplifying 8t2 + 7t + -10 = 0 Reorder the terms: -10 + 7t + 8t2 = 0 Solving -10 + 7t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -1.25 + 0.875t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + 0.875t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + 0.875t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + 0.875t + t2 = 0 + 1.25 0.875t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 0.875t + t2 = 1.25 The t term is 0.875t. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875t + 0.19140625 + t2 = 1.25 + 0.19140625 Reorder the terms: 0.19140625 + 0.875t + t2 = 1.25 + 0.19140625 Combine like terms: 1.25 + 0.19140625 = 1.44140625 0.19140625 + 0.875t + t2 = 1.44140625 Factor a perfect square on the left side: (t + 0.4375)(t + 0.4375) = 1.44140625 Calculate the square root of the right side: 1.200585795 Break this problem into two subproblems by setting (t + 0.4375) equal to 1.200585795 and -1.200585795.Subproblem 1
t + 0.4375 = 1.200585795 Simplifying t + 0.4375 = 1.200585795 Reorder the terms: 0.4375 + t = 1.200585795 Solving 0.4375 + t = 1.200585795 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + t = 1.200585795 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = 1.200585795 + -0.4375 t = 1.200585795 + -0.4375 Combine like terms: 1.200585795 + -0.4375 = 0.763085795 t = 0.763085795 Simplifying t = 0.763085795Subproblem 2
t + 0.4375 = -1.200585795 Simplifying t + 0.4375 = -1.200585795 Reorder the terms: 0.4375 + t = -1.200585795 Solving 0.4375 + t = -1.200585795 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + t = -1.200585795 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + t = -1.200585795 + -0.4375 t = -1.200585795 + -0.4375 Combine like terms: -1.200585795 + -0.4375 = -1.638085795 t = -1.638085795 Simplifying t = -1.638085795Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.763085795, -1.638085795}
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