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Simplifying (6) = t2 + 2t + 4 6 = t2 + 2t + 4 Reorder the terms: 6 = 4 + 2t + t2 Solving 6 = 4 + 2t + t2 Solving for variable 't'. Combine like terms: 6 + -4 = 2 2 + -2t + -1t2 = 4 + 2t + t2 + -4 + -2t + -1t2 Reorder the terms: 2 + -2t + -1t2 = 4 + -4 + 2t + -2t + t2 + -1t2 Combine like terms: 4 + -4 = 0 2 + -2t + -1t2 = 0 + 2t + -2t + t2 + -1t2 2 + -2t + -1t2 = 2t + -2t + t2 + -1t2 Combine like terms: 2t + -2t = 0 2 + -2t + -1t2 = 0 + t2 + -1t2 2 + -2t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 2 + -2t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -2 + 2t + t2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + 2t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2t + t2 = 0 + 2 2t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 2t + t2 = 2 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 = 2 + 1 Reorder the terms: 1 + 2t + t2 = 2 + 1 Combine like terms: 2 + 1 = 3 1 + 2t + t2 = 3 Factor a perfect square on the left side: (t + 1)(t + 1) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (t + 1) equal to 1.732050808 and -1.732050808.Subproblem 1
t + 1 = 1.732050808 Simplifying t + 1 = 1.732050808 Reorder the terms: 1 + t = 1.732050808 Solving 1 + t = 1.732050808 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 = 1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + t = 1.732050808 + -1 t = 1.732050808 + -1 Combine like terms: 1.732050808 + -1 = 0.732050808 t = 0.732050808 Simplifying t = 0.732050808Subproblem 2
t + 1 = -1.732050808 Simplifying t + 1 = -1.732050808 Reorder the terms: 1 + t = -1.732050808 Solving 1 + t = -1.732050808 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 = -1.732050808 + -1 Combine like terms: 1 + -1 = 0 0 + t = -1.732050808 + -1 t = -1.732050808 + -1 Combine like terms: -1.732050808 + -1 = -2.732050808 t = -2.732050808 Simplifying t = -2.732050808Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.732050808, -2.732050808}
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