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Simplifying 2t2 + -5t = 30 Reorder the terms: -5t + 2t2 = 30 Solving -5t + 2t2 = 30 Solving for variable 't'. Reorder the terms: -30 + -5t + 2t2 = 30 + -30 Combine like terms: 30 + -30 = 0 -30 + -5t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15 + -2.5t + t2 = 0 Move the constant term to the right: Add '15' to each side of the equation. -15 + -2.5t + 15 + t2 = 0 + 15 Reorder the terms: -15 + 15 + -2.5t + t2 = 0 + 15 Combine like terms: -15 + 15 = 0 0 + -2.5t + t2 = 0 + 15 -2.5t + t2 = 0 + 15 Combine like terms: 0 + 15 = 15 -2.5t + t2 = 15 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = 15 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 15 + 1.5625 Combine like terms: 15 + 1.5625 = 16.5625 1.5625 + -2.5t + t2 = 16.5625 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 16.5625 Calculate the square root of the right side: 4.069705149 Break this problem into two subproblems by setting (t + -1.25) equal to 4.069705149 and -4.069705149.Subproblem 1
t + -1.25 = 4.069705149 Simplifying t + -1.25 = 4.069705149 Reorder the terms: -1.25 + t = 4.069705149 Solving -1.25 + t = 4.069705149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 4.069705149 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 4.069705149 + 1.25 t = 4.069705149 + 1.25 Combine like terms: 4.069705149 + 1.25 = 5.319705149 t = 5.319705149 Simplifying t = 5.319705149Subproblem 2
t + -1.25 = -4.069705149 Simplifying t + -1.25 = -4.069705149 Reorder the terms: -1.25 + t = -4.069705149 Solving -1.25 + t = -4.069705149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -4.069705149 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -4.069705149 + 1.25 t = -4.069705149 + 1.25 Combine like terms: -4.069705149 + 1.25 = -2.819705149 t = -2.819705149 Simplifying t = -2.819705149Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.319705149, -2.819705149}
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