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Simplifying 0 = -2t2 + 10t + 5 Reorder the terms: 0 = 5 + 10t + -2t2 Solving 0 = 5 + 10t + -2t2 Solving for variable 't'. Combine like terms: 0 + -5 = -5 -5 + -10t + 2t2 = 5 + 10t + -2t2 + -5 + -10t + 2t2 Reorder the terms: -5 + -10t + 2t2 = 5 + -5 + 10t + -10t + -2t2 + 2t2 Combine like terms: 5 + -5 = 0 -5 + -10t + 2t2 = 0 + 10t + -10t + -2t2 + 2t2 -5 + -10t + 2t2 = 10t + -10t + -2t2 + 2t2 Combine like terms: 10t + -10t = 0 -5 + -10t + 2t2 = 0 + -2t2 + 2t2 -5 + -10t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -5 + -10t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -2.5 + -5t + t2 = 0 Move the constant term to the right: Add '2.5' to each side of the equation. -2.5 + -5t + 2.5 + t2 = 0 + 2.5 Reorder the terms: -2.5 + 2.5 + -5t + t2 = 0 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + -5t + t2 = 0 + 2.5 -5t + t2 = 0 + 2.5 Combine like terms: 0 + 2.5 = 2.5 -5t + t2 = 2.5 The t term is -5t. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5t + 6.25 + t2 = 2.5 + 6.25 Reorder the terms: 6.25 + -5t + t2 = 2.5 + 6.25 Combine like terms: 2.5 + 6.25 = 8.75 6.25 + -5t + t2 = 8.75 Factor a perfect square on the left side: (t + -2.5)(t + -2.5) = 8.75 Calculate the square root of the right side: 2.958039892 Break this problem into two subproblems by setting (t + -2.5) equal to 2.958039892 and -2.958039892.Subproblem 1
t + -2.5 = 2.958039892 Simplifying t + -2.5 = 2.958039892 Reorder the terms: -2.5 + t = 2.958039892 Solving -2.5 + t = 2.958039892 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = 2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = 2.958039892 + 2.5 t = 2.958039892 + 2.5 Combine like terms: 2.958039892 + 2.5 = 5.458039892 t = 5.458039892 Simplifying t = 5.458039892Subproblem 2
t + -2.5 = -2.958039892 Simplifying t + -2.5 = -2.958039892 Reorder the terms: -2.5 + t = -2.958039892 Solving -2.5 + t = -2.958039892 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + t = -2.958039892 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + t = -2.958039892 + 2.5 t = -2.958039892 + 2.5 Combine like terms: -2.958039892 + 2.5 = -0.458039892 t = -0.458039892 Simplifying t = -0.458039892Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.458039892, -0.458039892}
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