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Simplifying 2t2 + -55t + -375 = 0 Reorder the terms: -375 + -55t + 2t2 = 0 Solving -375 + -55t + 2t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -187.5 + -27.5t + t2 = 0 Move the constant term to the right: Add '187.5' to each side of the equation. -187.5 + -27.5t + 187.5 + t2 = 0 + 187.5 Reorder the terms: -187.5 + 187.5 + -27.5t + t2 = 0 + 187.5 Combine like terms: -187.5 + 187.5 = 0.0 0.0 + -27.5t + t2 = 0 + 187.5 -27.5t + t2 = 0 + 187.5 Combine like terms: 0 + 187.5 = 187.5 -27.5t + t2 = 187.5 The t term is -27.5t. Take half its coefficient (-13.75). Square it (189.0625) and add it to both sides. Add '189.0625' to each side of the equation. -27.5t + 189.0625 + t2 = 187.5 + 189.0625 Reorder the terms: 189.0625 + -27.5t + t2 = 187.5 + 189.0625 Combine like terms: 187.5 + 189.0625 = 376.5625 189.0625 + -27.5t + t2 = 376.5625 Factor a perfect square on the left side: (t + -13.75)(t + -13.75) = 376.5625 Calculate the square root of the right side: 19.40521837 Break this problem into two subproblems by setting (t + -13.75) equal to 19.40521837 and -19.40521837.Subproblem 1
t + -13.75 = 19.40521837 Simplifying t + -13.75 = 19.40521837 Reorder the terms: -13.75 + t = 19.40521837 Solving -13.75 + t = 19.40521837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + t = 19.40521837 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + t = 19.40521837 + 13.75 t = 19.40521837 + 13.75 Combine like terms: 19.40521837 + 13.75 = 33.15521837 t = 33.15521837 Simplifying t = 33.15521837Subproblem 2
t + -13.75 = -19.40521837 Simplifying t + -13.75 = -19.40521837 Reorder the terms: -13.75 + t = -19.40521837 Solving -13.75 + t = -19.40521837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + t = -19.40521837 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + t = -19.40521837 + 13.75 t = -19.40521837 + 13.75 Combine like terms: -19.40521837 + 13.75 = -5.65521837 t = -5.65521837 Simplifying t = -5.65521837Solution
The solution to the problem is based on the solutions from the subproblems. t = {33.15521837, -5.65521837}
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