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Simplifying t2 + -2t + -100 = 0 Reorder the terms: -100 + -2t + t2 = 0 Solving -100 + -2t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + -2t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + -2t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -2t + t2 = 0 + 100 -2t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 -2t + t2 = 100 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = 100 + 1 Reorder the terms: 1 + -2t + t2 = 100 + 1 Combine like terms: 100 + 1 = 101 1 + -2t + t2 = 101 Factor a perfect square on the left side: (t + -1)(t + -1) = 101 Calculate the square root of the right side: 10.049875621 Break this problem into two subproblems by setting (t + -1) equal to 10.049875621 and -10.049875621.Subproblem 1
t + -1 = 10.049875621 Simplifying t + -1 = 10.049875621 Reorder the terms: -1 + t = 10.049875621 Solving -1 + t = 10.049875621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 10.049875621 + 1 Combine like terms: -1 + 1 = 0 0 + t = 10.049875621 + 1 t = 10.049875621 + 1 Combine like terms: 10.049875621 + 1 = 11.049875621 t = 11.049875621 Simplifying t = 11.049875621Subproblem 2
t + -1 = -10.049875621 Simplifying t + -1 = -10.049875621 Reorder the terms: -1 + t = -10.049875621 Solving -1 + t = -10.049875621 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -10.049875621 + 1 Combine like terms: -1 + 1 = 0 0 + t = -10.049875621 + 1 t = -10.049875621 + 1 Combine like terms: -10.049875621 + 1 = -9.049875621 t = -9.049875621 Simplifying t = -9.049875621Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.049875621, -9.049875621}
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