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Simplifying -2t2 + 110t = 5 Reorder the terms: 110t + -2t2 = 5 Solving 110t + -2t2 = 5 Solving for variable 't'. Reorder the terms: -5 + 110t + -2t2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + 110t + -2t2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. 2.5 + -55t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + -55t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + -55t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + -55t + t2 = 0 + -2.5 -55t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 -55t + t2 = -2.5 The t term is -55t. Take half its coefficient (-27.5). Square it (756.25) and add it to both sides. Add '756.25' to each side of the equation. -55t + 756.25 + t2 = -2.5 + 756.25 Reorder the terms: 756.25 + -55t + t2 = -2.5 + 756.25 Combine like terms: -2.5 + 756.25 = 753.75 756.25 + -55t + t2 = 753.75 Factor a perfect square on the left side: (t + -27.5)(t + -27.5) = 753.75 Calculate the square root of the right side: 27.454507827 Break this problem into two subproblems by setting (t + -27.5) equal to 27.454507827 and -27.454507827.Subproblem 1
t + -27.5 = 27.454507827 Simplifying t + -27.5 = 27.454507827 Reorder the terms: -27.5 + t = 27.454507827 Solving -27.5 + t = 27.454507827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + t = 27.454507827 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + t = 27.454507827 + 27.5 t = 27.454507827 + 27.5 Combine like terms: 27.454507827 + 27.5 = 54.954507827 t = 54.954507827 Simplifying t = 54.954507827Subproblem 2
t + -27.5 = -27.454507827 Simplifying t + -27.5 = -27.454507827 Reorder the terms: -27.5 + t = -27.454507827 Solving -27.5 + t = -27.454507827 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '27.5' to each side of the equation. -27.5 + 27.5 + t = -27.454507827 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + t = -27.454507827 + 27.5 t = -27.454507827 + 27.5 Combine like terms: -27.454507827 + 27.5 = 0.045492173 t = 0.045492173 Simplifying t = 0.045492173Solution
The solution to the problem is based on the solutions from the subproblems. t = {54.954507827, 0.045492173}
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