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Simplifying t2 + -20t + 21 = 0 Reorder the terms: 21 + -20t + t2 = 0 Solving 21 + -20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-21' to each side of the equation. 21 + -20t + -21 + t2 = 0 + -21 Reorder the terms: 21 + -21 + -20t + t2 = 0 + -21 Combine like terms: 21 + -21 = 0 0 + -20t + t2 = 0 + -21 -20t + t2 = 0 + -21 Combine like terms: 0 + -21 = -21 -20t + t2 = -21 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 = -21 + 100 Reorder the terms: 100 + -20t + t2 = -21 + 100 Combine like terms: -21 + 100 = 79 100 + -20t + t2 = 79 Factor a perfect square on the left side: (t + -10)(t + -10) = 79 Calculate the square root of the right side: 8.888194417 Break this problem into two subproblems by setting (t + -10) equal to 8.888194417 and -8.888194417.Subproblem 1
t + -10 = 8.888194417 Simplifying t + -10 = 8.888194417 Reorder the terms: -10 + t = 8.888194417 Solving -10 + t = 8.888194417 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 = 8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + t = 8.888194417 + 10 t = 8.888194417 + 10 Combine like terms: 8.888194417 + 10 = 18.888194417 t = 18.888194417 Simplifying t = 18.888194417Subproblem 2
t + -10 = -8.888194417 Simplifying t + -10 = -8.888194417 Reorder the terms: -10 + t = -8.888194417 Solving -10 + t = -8.888194417 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 = -8.888194417 + 10 Combine like terms: -10 + 10 = 0 0 + t = -8.888194417 + 10 t = -8.888194417 + 10 Combine like terms: -8.888194417 + 10 = 1.111805583 t = 1.111805583 Simplifying t = 1.111805583Solution
The solution to the problem is based on the solutions from the subproblems. t = {18.888194417, 1.111805583}
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