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Simplifying t2 + -31t + 236 = 0 Reorder the terms: 236 + -31t + t2 = 0 Solving 236 + -31t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-236' to each side of the equation. 236 + -31t + -236 + t2 = 0 + -236 Reorder the terms: 236 + -236 + -31t + t2 = 0 + -236 Combine like terms: 236 + -236 = 0 0 + -31t + t2 = 0 + -236 -31t + t2 = 0 + -236 Combine like terms: 0 + -236 = -236 -31t + t2 = -236 The t term is -31t. Take half its coefficient (-15.5). Square it (240.25) and add it to both sides. Add '240.25' to each side of the equation. -31t + 240.25 + t2 = -236 + 240.25 Reorder the terms: 240.25 + -31t + t2 = -236 + 240.25 Combine like terms: -236 + 240.25 = 4.25 240.25 + -31t + t2 = 4.25 Factor a perfect square on the left side: (t + -15.5)(t + -15.5) = 4.25 Calculate the square root of the right side: 2.061552813 Break this problem into two subproblems by setting (t + -15.5) equal to 2.061552813 and -2.061552813.Subproblem 1
t + -15.5 = 2.061552813 Simplifying t + -15.5 = 2.061552813 Reorder the terms: -15.5 + t = 2.061552813 Solving -15.5 + t = 2.061552813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = 2.061552813 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = 2.061552813 + 15.5 t = 2.061552813 + 15.5 Combine like terms: 2.061552813 + 15.5 = 17.561552813 t = 17.561552813 Simplifying t = 17.561552813Subproblem 2
t + -15.5 = -2.061552813 Simplifying t + -15.5 = -2.061552813 Reorder the terms: -15.5 + t = -2.061552813 Solving -15.5 + t = -2.061552813 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '15.5' to each side of the equation. -15.5 + 15.5 + t = -2.061552813 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + t = -2.061552813 + 15.5 t = -2.061552813 + 15.5 Combine like terms: -2.061552813 + 15.5 = 13.438447187 t = 13.438447187 Simplifying t = 13.438447187Solution
The solution to the problem is based on the solutions from the subproblems. t = {17.561552813, 13.438447187}
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