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Simplifying t2 + 19t + 10 = 0 Reorder the terms: 10 + 19t + t2 = 0 Solving 10 + 19t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 19t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + 19t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 19t + t2 = 0 + -10 19t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 19t + t2 = -10 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 = -10 + 90.25 Reorder the terms: 90.25 + 19t + t2 = -10 + 90.25 Combine like terms: -10 + 90.25 = 80.25 90.25 + 19t + t2 = 80.25 Factor a perfect square on the left side: (t + 9.5)(t + 9.5) = 80.25 Calculate the square root of the right side: 8.958236434 Break this problem into two subproblems by setting (t + 9.5) equal to 8.958236434 and -8.958236434.Subproblem 1
t + 9.5 = 8.958236434 Simplifying t + 9.5 = 8.958236434 Reorder the terms: 9.5 + t = 8.958236434 Solving 9.5 + t = 8.958236434 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 = 8.958236434 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + t = 8.958236434 + -9.5 t = 8.958236434 + -9.5 Combine like terms: 8.958236434 + -9.5 = -0.541763566 t = -0.541763566 Simplifying t = -0.541763566Subproblem 2
t + 9.5 = -8.958236434 Simplifying t + 9.5 = -8.958236434 Reorder the terms: 9.5 + t = -8.958236434 Solving 9.5 + t = -8.958236434 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 = -8.958236434 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + t = -8.958236434 + -9.5 t = -8.958236434 + -9.5 Combine like terms: -8.958236434 + -9.5 = -18.458236434 t = -18.458236434 Simplifying t = -18.458236434Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.541763566, -18.458236434}
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