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Simplifying t2 + 15t + -200 = 0 Reorder the terms: -200 + 15t + t2 = 0 Solving -200 + 15t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '200' to each side of the equation. -200 + 15t + 200 + t2 = 0 + 200 Reorder the terms: -200 + 200 + 15t + t2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 15t + t2 = 0 + 200 15t + t2 = 0 + 200 Combine like terms: 0 + 200 = 200 15t + t2 = 200 The t term is 15t. Take half its coefficient (7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. 15t + 56.25 + t2 = 200 + 56.25 Reorder the terms: 56.25 + 15t + t2 = 200 + 56.25 Combine like terms: 200 + 56.25 = 256.25 56.25 + 15t + t2 = 256.25 Factor a perfect square on the left side: (t + 7.5)(t + 7.5) = 256.25 Calculate the square root of the right side: 16.007810594 Break this problem into two subproblems by setting (t + 7.5) equal to 16.007810594 and -16.007810594.Subproblem 1
t + 7.5 = 16.007810594 Simplifying t + 7.5 = 16.007810594 Reorder the terms: 7.5 + t = 16.007810594 Solving 7.5 + t = 16.007810594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = 16.007810594 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = 16.007810594 + -7.5 t = 16.007810594 + -7.5 Combine like terms: 16.007810594 + -7.5 = 8.507810594 t = 8.507810594 Simplifying t = 8.507810594Subproblem 2
t + 7.5 = -16.007810594 Simplifying t + 7.5 = -16.007810594 Reorder the terms: 7.5 + t = -16.007810594 Solving 7.5 + t = -16.007810594 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.5' to each side of the equation. 7.5 + -7.5 + t = -16.007810594 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + t = -16.007810594 + -7.5 t = -16.007810594 + -7.5 Combine like terms: -16.007810594 + -7.5 = -23.507810594 t = -23.507810594 Simplifying t = -23.507810594Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.507810594, -23.507810594}
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