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Simplifying 20 = t2 + 2t Reorder the terms: 20 = 2t + t2 Solving 20 = 2t + t2 Solving for variable 't'. Reorder the terms: 20 + -2t + -1t2 = 2t + -2t + t2 + -1t2 Combine like terms: 2t + -2t = 0 20 + -2t + -1t2 = 0 + t2 + -1t2 20 + -2t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 20 + -2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -20 + 2t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + 2t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + 2t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + 2t + t2 = 0 + 20 2t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 2t + t2 = 20 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 = 20 + 1 Reorder the terms: 1 + 2t + t2 = 20 + 1 Combine like terms: 20 + 1 = 21 1 + 2t + t2 = 21 Factor a perfect square on the left side: (t + 1)(t + 1) = 21 Calculate the square root of the right side: 4.582575695 Break this problem into two subproblems by setting (t + 1) equal to 4.582575695 and -4.582575695.Subproblem 1
t + 1 = 4.582575695 Simplifying t + 1 = 4.582575695 Reorder the terms: 1 + t = 4.582575695 Solving 1 + t = 4.582575695 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 = 4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + t = 4.582575695 + -1 t = 4.582575695 + -1 Combine like terms: 4.582575695 + -1 = 3.582575695 t = 3.582575695 Simplifying t = 3.582575695Subproblem 2
t + 1 = -4.582575695 Simplifying t + 1 = -4.582575695 Reorder the terms: 1 + t = -4.582575695 Solving 1 + t = -4.582575695 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 = -4.582575695 + -1 Combine like terms: 1 + -1 = 0 0 + t = -4.582575695 + -1 t = -4.582575695 + -1 Combine like terms: -4.582575695 + -1 = -5.582575695 t = -5.582575695 Simplifying t = -5.582575695Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.582575695, -5.582575695}
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