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Simplifying t2 + -6 + -2t + -20 = 0 Reorder the terms: -6 + -20 + -2t + t2 = 0 Combine like terms: -6 + -20 = -26 -26 + -2t + t2 = 0 Solving -26 + -2t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '26' to each side of the equation. -26 + -2t + 26 + t2 = 0 + 26 Reorder the terms: -26 + 26 + -2t + t2 = 0 + 26 Combine like terms: -26 + 26 = 0 0 + -2t + t2 = 0 + 26 -2t + t2 = 0 + 26 Combine like terms: 0 + 26 = 26 -2t + t2 = 26 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 = 26 + 1 Reorder the terms: 1 + -2t + t2 = 26 + 1 Combine like terms: 26 + 1 = 27 1 + -2t + t2 = 27 Factor a perfect square on the left side: (t + -1)(t + -1) = 27 Calculate the square root of the right side: 5.196152423 Break this problem into two subproblems by setting (t + -1) equal to 5.196152423 and -5.196152423.Subproblem 1
t + -1 = 5.196152423 Simplifying t + -1 = 5.196152423 Reorder the terms: -1 + t = 5.196152423 Solving -1 + t = 5.196152423 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 = 5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + t = 5.196152423 + 1 t = 5.196152423 + 1 Combine like terms: 5.196152423 + 1 = 6.196152423 t = 6.196152423 Simplifying t = 6.196152423Subproblem 2
t + -1 = -5.196152423 Simplifying t + -1 = -5.196152423 Reorder the terms: -1 + t = -5.196152423 Solving -1 + t = -5.196152423 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 = -5.196152423 + 1 Combine like terms: -1 + 1 = 0 0 + t = -5.196152423 + 1 t = -5.196152423 + 1 Combine like terms: -5.196152423 + 1 = -4.196152423 t = -4.196152423 Simplifying t = -4.196152423Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.196152423, -4.196152423}
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