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Simplifying t2 + -20t + -1 = 0 Reorder the terms: -1 + -20t + t2 = 0 Solving -1 + -20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -20t + 1 + t2 = 0 + 1 Reorder the terms: -1 + 1 + -20t + t2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -20t + t2 = 0 + 1 -20t + t2 = 0 + 1 Combine like terms: 0 + 1 = 1 -20t + t2 = 1 The t term is -20t. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20t + 100 + t2 = 1 + 100 Reorder the terms: 100 + -20t + t2 = 1 + 100 Combine like terms: 1 + 100 = 101 100 + -20t + t2 = 101 Factor a perfect square on the left side: (t + -10)(t + -10) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (t + -10) equal to 10.049875621 and -10.049875621.Subproblem 1
t + -10 = 10.049875621 Simplifying t + -10 = 10.049875621 Reorder the terms: -10 + t = 10.049875621 Solving -10 + t = 10.049875621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = 10.049875621 + 10 Combine like terms: -10 + 10 = 0 0 + t = 10.049875621 + 10 t = 10.049875621 + 10 Combine like terms: 10.049875621 + 10 = 20.049875621 t = 20.049875621 Simplifying t = 20.049875621Subproblem 2
t + -10 = -10.049875621 Simplifying t + -10 = -10.049875621 Reorder the terms: -10 + t = -10.049875621 Solving -10 + t = -10.049875621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + t = -10.049875621 + 10 Combine like terms: -10 + 10 = 0 0 + t = -10.049875621 + 10 t = -10.049875621 + 10 Combine like terms: -10.049875621 + 10 = -0.049875621 t = -0.049875621 Simplifying t = -0.049875621Solution
The solution to the problem is based on the solutions from the subproblems. t = {20.049875621, -0.049875621}
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