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Simplifying 2t2 + 19t + 5 = 0 Reorder the terms: 5 + 19t + 2t2 = 0 Solving 5 + 19t + 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'. 2.5 + 9.5t + t2 = 0 Move the constant term to the right: Add '-2.5' to each side of the equation. 2.5 + 9.5t + -2.5 + t2 = 0 + -2.5 Reorder the terms: 2.5 + -2.5 + 9.5t + t2 = 0 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + 9.5t + t2 = 0 + -2.5 9.5t + t2 = 0 + -2.5 Combine like terms: 0 + -2.5 = -2.5 9.5t + t2 = -2.5 The t term is 9.5t. Take half its coefficient (4.75). Square it (22.5625) and add it to both sides. Add '22.5625' to each side of the equation. 9.5t + 22.5625 + t2 = -2.5 + 22.5625 Reorder the terms: 22.5625 + 9.5t + t2 = -2.5 + 22.5625 Combine like terms: -2.5 + 22.5625 = 20.0625 22.5625 + 9.5t + t2 = 20.0625 Factor a perfect square on the left side: (t + 4.75)(t + 4.75) = 20.0625 Calculate the square root of the right side: 4.479118217 Break this problem into two subproblems by setting (t + 4.75) equal to 4.479118217 and -4.479118217.Subproblem 1
t + 4.75 = 4.479118217 Simplifying t + 4.75 = 4.479118217 Reorder the terms: 4.75 + t = 4.479118217 Solving 4.75 + t = 4.479118217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + t = 4.479118217 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + t = 4.479118217 + -4.75 t = 4.479118217 + -4.75 Combine like terms: 4.479118217 + -4.75 = -0.270881783 t = -0.270881783 Simplifying t = -0.270881783Subproblem 2
t + 4.75 = -4.479118217 Simplifying t + 4.75 = -4.479118217 Reorder the terms: 4.75 + t = -4.479118217 Solving 4.75 + t = -4.479118217 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-4.75' to each side of the equation. 4.75 + -4.75 + t = -4.479118217 + -4.75 Combine like terms: 4.75 + -4.75 = 0.00 0.00 + t = -4.479118217 + -4.75 t = -4.479118217 + -4.75 Combine like terms: -4.479118217 + -4.75 = -9.229118217 t = -9.229118217 Simplifying t = -9.229118217Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.270881783, -9.229118217}
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