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Simplifying -1t2 + 31t + 125 = 0 Reorder the terms: 125 + 31t + -1t2 = 0 Solving 125 + 31t + -1t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -125 + -31t + t2 = 0 Move the constant term to the right: Add '125' to each side of the equation. -125 + -31t + 125 + t2 = 0 + 125 Reorder the terms: -125 + 125 + -31t + t2 = 0 + 125 Combine like terms: -125 + 125 = 0 0 + -31t + t2 = 0 + 125 -31t + t2 = 0 + 125 Combine like terms: 0 + 125 = 125 -31t + t2 = 125 The t term is -31t. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31t + 240.25 + t2 = 125 + 240.25 Reorder the terms: 240.25 + -31t + t2 = 125 + 240.25 Combine like terms: 125 + 240.25 = 365.25 240.25 + -31t + t2 = 365.25 Factor a perfect square on the left side: (t + -15.5)(t + -15.5) = 365.25 Calculate the square root of the right side: 19.111514854 Break this problem into two subproblems by setting (t + -15.5) equal to 19.111514854 and -19.111514854.Subproblem 1
t + -15.5 = 19.111514854 Simplifying t + -15.5 = 19.111514854 Reorder the terms: -15.5 + t = 19.111514854 Solving -15.5 + t = 19.111514854 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = 19.111514854 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = 19.111514854 + 15.5 t = 19.111514854 + 15.5 Combine like terms: 19.111514854 + 15.5 = 34.611514854 t = 34.611514854 Simplifying t = 34.611514854Subproblem 2
t + -15.5 = -19.111514854 Simplifying t + -15.5 = -19.111514854 Reorder the terms: -15.5 + t = -19.111514854 Solving -15.5 + t = -19.111514854 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = -19.111514854 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = -19.111514854 + 15.5 t = -19.111514854 + 15.5 Combine like terms: -19.111514854 + 15.5 = -3.611514854 t = -3.611514854 Simplifying t = -3.611514854Solution
The solution to the problem is based on the solutions from the subproblems. t = {34.611514854, -3.611514854}
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