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Simplifying t2 + 3t + -200 = 0 Reorder the terms: -200 + 3t + t2 = 0 Solving -200 + 3t + 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 + 3t + 200 + t2 = 0 + 200 Reorder the terms: -200 + 200 + 3t + t2 = 0 + 200 Combine like terms: -200 + 200 = 0 0 + 3t + t2 = 0 + 200 3t + t2 = 0 + 200 Combine like terms: 0 + 200 = 200 3t + t2 = 200 The t term is 3t. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3t + 2.25 + t2 = 200 + 2.25 Reorder the terms: 2.25 + 3t + t2 = 200 + 2.25 Combine like terms: 200 + 2.25 = 202.25 2.25 + 3t + t2 = 202.25 Factor a perfect square on the left side: (t + 1.5)(t + 1.5) = 202.25 Calculate the square root of the right side: 14.221462653 Break this problem into two subproblems by setting (t + 1.5) equal to 14.221462653 and -14.221462653.Subproblem 1
t + 1.5 = 14.221462653 Simplifying t + 1.5 = 14.221462653 Reorder the terms: 1.5 + t = 14.221462653 Solving 1.5 + t = 14.221462653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = 14.221462653 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = 14.221462653 + -1.5 t = 14.221462653 + -1.5 Combine like terms: 14.221462653 + -1.5 = 12.721462653 t = 12.721462653 Simplifying t = 12.721462653Subproblem 2
t + 1.5 = -14.221462653 Simplifying t + 1.5 = -14.221462653 Reorder the terms: 1.5 + t = -14.221462653 Solving 1.5 + t = -14.221462653 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + t = -14.221462653 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + t = -14.221462653 + -1.5 t = -14.221462653 + -1.5 Combine like terms: -14.221462653 + -1.5 = -15.721462653 t = -15.721462653 Simplifying t = -15.721462653Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.721462653, -15.721462653}
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