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Simplifying t2 + -8t + -2 = 0 Reorder the terms: -2 + -8t + t2 = 0 Solving -2 + -8t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -8t + 2 + t2 = 0 + 2 Reorder the terms: -2 + 2 + -8t + t2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -8t + t2 = 0 + 2 -8t + t2 = 0 + 2 Combine like terms: 0 + 2 = 2 -8t + t2 = 2 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 = 2 + 16 Reorder the terms: 16 + -8t + t2 = 2 + 16 Combine like terms: 2 + 16 = 18 16 + -8t + t2 = 18 Factor a perfect square on the left side: (t + -4)(t + -4) = 18 Calculate the square root of the right side: 4.242640687 Break this problem into two subproblems by setting (t + -4) equal to 4.242640687 and -4.242640687.Subproblem 1
t + -4 = 4.242640687 Simplifying t + -4 = 4.242640687 Reorder the terms: -4 + t = 4.242640687 Solving -4 + t = 4.242640687 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 = 4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + t = 4.242640687 + 4 t = 4.242640687 + 4 Combine like terms: 4.242640687 + 4 = 8.242640687 t = 8.242640687 Simplifying t = 8.242640687Subproblem 2
t + -4 = -4.242640687 Simplifying t + -4 = -4.242640687 Reorder the terms: -4 + t = -4.242640687 Solving -4 + t = -4.242640687 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 = -4.242640687 + 4 Combine like terms: -4 + 4 = 0 0 + t = -4.242640687 + 4 t = -4.242640687 + 4 Combine like terms: -4.242640687 + 4 = -0.242640687 t = -0.242640687 Simplifying t = -0.242640687Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.242640687, -0.242640687}
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