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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 = 18.458236434 t = 18.458236434 Simplifying t = 18.458236434Subproblem 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 = 0.541763566 t = 0.541763566 Simplifying t = 0.541763566Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.458236434, 0.541763566}
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