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Simplifying t2 + -108t + -3950 = 0 Reorder the terms: -3950 + -108t + t2 = 0 Solving -3950 + -108t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '3950' to each side of the equation. -3950 + -108t + 3950 + t2 = 0 + 3950 Reorder the terms: -3950 + 3950 + -108t + t2 = 0 + 3950 Combine like terms: -3950 + 3950 = 0 0 + -108t + t2 = 0 + 3950 -108t + t2 = 0 + 3950 Combine like terms: 0 + 3950 = 3950 -108t + t2 = 3950 The t term is -108t. Take half its coefficient (-54). Square it (2916) and add it to both sides. Add '2916' to each side of the equation. -108t + 2916 + t2 = 3950 + 2916 Reorder the terms: 2916 + -108t + t2 = 3950 + 2916 Combine like terms: 3950 + 2916 = 6866 2916 + -108t + t2 = 6866 Factor a perfect square on the left side: (t + -54)(t + -54) = 6866 Calculate the square root of the right side: 82.861329943 Break this problem into two subproblems by setting (t + -54) equal to 82.861329943 and -82.861329943.Subproblem 1
t + -54 = 82.861329943 Simplifying t + -54 = 82.861329943 Reorder the terms: -54 + t = 82.861329943 Solving -54 + t = 82.861329943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + t = 82.861329943 + 54 Combine like terms: -54 + 54 = 0 0 + t = 82.861329943 + 54 t = 82.861329943 + 54 Combine like terms: 82.861329943 + 54 = 136.861329943 t = 136.861329943 Simplifying t = 136.861329943Subproblem 2
t + -54 = -82.861329943 Simplifying t + -54 = -82.861329943 Reorder the terms: -54 + t = -82.861329943 Solving -54 + t = -82.861329943 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '54' to each side of the equation. -54 + 54 + t = -82.861329943 + 54 Combine like terms: -54 + 54 = 0 0 + t = -82.861329943 + 54 t = -82.861329943 + 54 Combine like terms: -82.861329943 + 54 = -28.861329943 t = -28.861329943 Simplifying t = -28.861329943Solution
The solution to the problem is based on the solutions from the subproblems. t = {136.861329943, -28.861329943}
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