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Simplifying t2 + 19t + 19 = 0 Reorder the terms: 19 + 19t + t2 = 0 Solving 19 + 19t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-19' to each side of the equation. 19 + 19t + -19 + t2 = 0 + -19 Reorder the terms: 19 + -19 + 19t + t2 = 0 + -19 Combine like terms: 19 + -19 = 0 0 + 19t + t2 = 0 + -19 19t + t2 = 0 + -19 Combine like terms: 0 + -19 = -19 19t + t2 = -19 The t term is 19t. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19t + 90.25 + t2 = -19 + 90.25 Reorder the terms: 90.25 + 19t + t2 = -19 + 90.25 Combine like terms: -19 + 90.25 = 71.25 90.25 + 19t + t2 = 71.25 Factor a perfect square on the left side: (t + 9.5)(t + 9.5) = 71.25 Calculate the square root of the right side: 8.440971508 Break this problem into two subproblems by setting (t + 9.5) equal to 8.440971508 and -8.440971508.Subproblem 1
t + 9.5 = 8.440971508 Simplifying t + 9.5 = 8.440971508 Reorder the terms: 9.5 + t = 8.440971508 Solving 9.5 + t = 8.440971508 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + t = 8.440971508 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + t = 8.440971508 + -9.5 t = 8.440971508 + -9.5 Combine like terms: 8.440971508 + -9.5 = -1.059028492 t = -1.059028492 Simplifying t = -1.059028492Subproblem 2
t + 9.5 = -8.440971508 Simplifying t + 9.5 = -8.440971508 Reorder the terms: 9.5 + t = -8.440971508 Solving 9.5 + t = -8.440971508 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + t = -8.440971508 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + t = -8.440971508 + -9.5 t = -8.440971508 + -9.5 Combine like terms: -8.440971508 + -9.5 = -17.940971508 t = -17.940971508 Simplifying t = -17.940971508Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.059028492, -17.940971508}
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