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Simplifying 2t2 + -2t + -13 = 0 Reorder the terms: -13 + -2t + 2t2 = 0 Solving -13 + -2t + 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'. -6.5 + -1t + t2 = 0 Move the constant term to the right: Add '6.5' to each side of the equation. -6.5 + -1t + 6.5 + t2 = 0 + 6.5 Reorder the terms: -6.5 + 6.5 + -1t + t2 = 0 + 6.5 Combine like terms: -6.5 + 6.5 = 0.0 0.0 + -1t + t2 = 0 + 6.5 -1t + t2 = 0 + 6.5 Combine like terms: 0 + 6.5 = 6.5 -1t + t2 = 6.5 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 6.5 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 6.5 + 0.25 Combine like terms: 6.5 + 0.25 = 6.75 0.25 + -1t + t2 = 6.75 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (t + -0.5) equal to 2.598076211 and -2.598076211.Subproblem 1
t + -0.5 = 2.598076211 Simplifying t + -0.5 = 2.598076211 Reorder the terms: -0.5 + t = 2.598076211 Solving -0.5 + t = 2.598076211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 2.598076211 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 2.598076211 + 0.5 t = 2.598076211 + 0.5 Combine like terms: 2.598076211 + 0.5 = 3.098076211 t = 3.098076211 Simplifying t = 3.098076211Subproblem 2
t + -0.5 = -2.598076211 Simplifying t + -0.5 = -2.598076211 Reorder the terms: -0.5 + t = -2.598076211 Solving -0.5 + t = -2.598076211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -2.598076211 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -2.598076211 + 0.5 t = -2.598076211 + 0.5 Combine like terms: -2.598076211 + 0.5 = -2.098076211 t = -2.098076211 Simplifying t = -2.098076211Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.098076211, -2.098076211}
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