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Simplifying 8t2 + 15t + -450 = 0 Reorder the terms: -450 + 15t + 8t2 = 0 Solving -450 + 15t + 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'. -56.25 + 1.875t + t2 = 0 Move the constant term to the right: Add '56.25' to each side of the equation. -56.25 + 1.875t + 56.25 + t2 = 0 + 56.25 Reorder the terms: -56.25 + 56.25 + 1.875t + t2 = 0 + 56.25 Combine like terms: -56.25 + 56.25 = 0.00 0.00 + 1.875t + t2 = 0 + 56.25 1.875t + t2 = 0 + 56.25 Combine like terms: 0 + 56.25 = 56.25 1.875t + t2 = 56.25 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 = 56.25 + 0.87890625 Reorder the terms: 0.87890625 + 1.875t + t2 = 56.25 + 0.87890625 Combine like terms: 56.25 + 0.87890625 = 57.12890625 0.87890625 + 1.875t + t2 = 57.12890625 Factor a perfect square on the left side: (t + 0.9375)(t + 0.9375) = 57.12890625 Calculate the square root of the right side: 7.558366639 Break this problem into two subproblems by setting (t + 0.9375) equal to 7.558366639 and -7.558366639.Subproblem 1
t + 0.9375 = 7.558366639 Simplifying t + 0.9375 = 7.558366639 Reorder the terms: 0.9375 + t = 7.558366639 Solving 0.9375 + t = 7.558366639 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 = 7.558366639 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = 7.558366639 + -0.9375 t = 7.558366639 + -0.9375 Combine like terms: 7.558366639 + -0.9375 = 6.620866639 t = 6.620866639 Simplifying t = 6.620866639Subproblem 2
t + 0.9375 = -7.558366639 Simplifying t + 0.9375 = -7.558366639 Reorder the terms: 0.9375 + t = -7.558366639 Solving 0.9375 + t = -7.558366639 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 = -7.558366639 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + t = -7.558366639 + -0.9375 t = -7.558366639 + -0.9375 Combine like terms: -7.558366639 + -0.9375 = -8.495866639 t = -8.495866639 Simplifying t = -8.495866639Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.620866639, -8.495866639}
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