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Simplifying t2 + -135t + -1125 = 0 Reorder the terms: -1125 + -135t + t2 = 0 Solving -1125 + -135t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1125' to each side of the equation. -1125 + -135t + 1125 + t2 = 0 + 1125 Reorder the terms: -1125 + 1125 + -135t + t2 = 0 + 1125 Combine like terms: -1125 + 1125 = 0 0 + -135t + t2 = 0 + 1125 -135t + t2 = 0 + 1125 Combine like terms: 0 + 1125 = 1125 -135t + t2 = 1125 The t term is -135t. Take half its coefficient (-67.5). Square it (4556.25) and add it to both sides. Add '4556.25' to each side of the equation. -135t + 4556.25 + t2 = 1125 + 4556.25 Reorder the terms: 4556.25 + -135t + t2 = 1125 + 4556.25 Combine like terms: 1125 + 4556.25 = 5681.25 4556.25 + -135t + t2 = 5681.25 Factor a perfect square on the left side: (t + -67.5)(t + -67.5) = 5681.25 Calculate the square root of the right side: 75.374067158 Break this problem into two subproblems by setting (t + -67.5) equal to 75.374067158 and -75.374067158.Subproblem 1
t + -67.5 = 75.374067158 Simplifying t + -67.5 = 75.374067158 Reorder the terms: -67.5 + t = 75.374067158 Solving -67.5 + t = 75.374067158 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '67.5' to each side of the equation. -67.5 + 67.5 + t = 75.374067158 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + t = 75.374067158 + 67.5 t = 75.374067158 + 67.5 Combine like terms: 75.374067158 + 67.5 = 142.874067158 t = 142.874067158 Simplifying t = 142.874067158Subproblem 2
t + -67.5 = -75.374067158 Simplifying t + -67.5 = -75.374067158 Reorder the terms: -67.5 + t = -75.374067158 Solving -67.5 + t = -75.374067158 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '67.5' to each side of the equation. -67.5 + 67.5 + t = -75.374067158 + 67.5 Combine like terms: -67.5 + 67.5 = 0.0 0.0 + t = -75.374067158 + 67.5 t = -75.374067158 + 67.5 Combine like terms: -75.374067158 + 67.5 = -7.874067158 t = -7.874067158 Simplifying t = -7.874067158Solution
The solution to the problem is based on the solutions from the subproblems. t = {142.874067158, -7.874067158}
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