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Simplifying 8t2 + -26t + -5 = 0 Reorder the terms: -5 + -26t + 8t2 = 0 Solving -5 + -26t + 8t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.625 + -3.25t + t2 = 0 Move the constant term to the right: Add '0.625' to each side of the equation. -0.625 + -3.25t + 0.625 + t2 = 0 + 0.625 Reorder the terms: -0.625 + 0.625 + -3.25t + t2 = 0 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + -3.25t + t2 = 0 + 0.625 -3.25t + t2 = 0 + 0.625 Combine like terms: 0 + 0.625 = 0.625 -3.25t + t2 = 0.625 The t term is -3.25t. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25t + 2.640625 + t2 = 0.625 + 2.640625 Reorder the terms: 2.640625 + -3.25t + t2 = 0.625 + 2.640625 Combine like terms: 0.625 + 2.640625 = 3.265625 2.640625 + -3.25t + t2 = 3.265625 Factor a perfect square on the left side: (t + -1.625)(t + -1.625) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (t + -1.625) equal to 1.807104037 and -1.807104037.Subproblem 1
t + -1.625 = 1.807104037 Simplifying t + -1.625 = 1.807104037 Reorder the terms: -1.625 + t = 1.807104037 Solving -1.625 + t = 1.807104037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = 1.807104037 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = 1.807104037 + 1.625 t = 1.807104037 + 1.625 Combine like terms: 1.807104037 + 1.625 = 3.432104037 t = 3.432104037 Simplifying t = 3.432104037Subproblem 2
t + -1.625 = -1.807104037 Simplifying t + -1.625 = -1.807104037 Reorder the terms: -1.625 + t = -1.807104037 Solving -1.625 + t = -1.807104037 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + t = -1.807104037 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + t = -1.807104037 + 1.625 t = -1.807104037 + 1.625 Combine like terms: -1.807104037 + 1.625 = -0.182104037 t = -0.182104037 Simplifying t = -0.182104037Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.432104037, -0.182104037}
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