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Simplifying (t + -4)(t + -4) = 2 Reorder the terms: (-4 + t)(t + -4) = 2 Reorder the terms: (-4 + t)(-4 + t) = 2 Multiply (-4 + t) * (-4 + t) (-4(-4 + t) + t(-4 + t)) = 2 ((-4 * -4 + t * -4) + t(-4 + t)) = 2 ((16 + -4t) + t(-4 + t)) = 2 (16 + -4t + (-4 * t + t * t)) = 2 (16 + -4t + (-4t + t2)) = 2 Combine like terms: -4t + -4t = -8t (16 + -8t + t2) = 2 Solving 16 + -8t + t2 = 2 Solving for variable 't'. Reorder the terms: 16 + -2 + -8t + t2 = 2 + -2 Combine like terms: 16 + -2 = 14 14 + -8t + t2 = 2 + -2 Combine like terms: 2 + -2 = 0 14 + -8t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-14' to each side of the equation. 14 + -8t + -14 + t2 = 0 + -14 Reorder the terms: 14 + -14 + -8t + t2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -8t + t2 = 0 + -14 -8t + t2 = 0 + -14 Combine like terms: 0 + -14 = -14 -8t + t2 = -14 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = -14 + 16 Reorder the terms: 16 + -8t + t2 = -14 + 16 Combine like terms: -14 + 16 = 2 16 + -8t + t2 = 2 Factor a perfect square on the left side: (t + -4)(t + -4) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (t + -4) equal to 1.414213562 and -1.414213562.Subproblem 1
t + -4 = 1.414213562 Simplifying t + -4 = 1.414213562 Reorder the terms: -4 + t = 1.414213562 Solving -4 + t = 1.414213562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + t = 1.414213562 + 4 t = 1.414213562 + 4 Combine like terms: 1.414213562 + 4 = 5.414213562 t = 5.414213562 Simplifying t = 5.414213562Subproblem 2
t + -4 = -1.414213562 Simplifying t + -4 = -1.414213562 Reorder the terms: -4 + t = -1.414213562 Solving -4 + t = -1.414213562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -1.414213562 + 4 Combine like terms: -4 + 4 = 0 0 + t = -1.414213562 + 4 t = -1.414213562 + 4 Combine like terms: -1.414213562 + 4 = 2.585786438 t = 2.585786438 Simplifying t = 2.585786438Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.414213562, 2.585786438}
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