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Simplifying t2 + 8t + 10 = 0 Reorder the terms: 10 + 8t + t2 = 0 Solving 10 + 8t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-10' to each side of the equation. 10 + 8t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + 8t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 8t + t2 = 0 + -10 8t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 8t + t2 = -10 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 = -10 + 16 Reorder the terms: 16 + 8t + t2 = -10 + 16 Combine like terms: -10 + 16 = 6 16 + 8t + t2 = 6 Factor a perfect square on the left side: (t + 4)(t + 4) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (t + 4) equal to 2.449489743 and -2.449489743.Subproblem 1
t + 4 = 2.449489743 Simplifying t + 4 = 2.449489743 Reorder the terms: 4 + t = 2.449489743 Solving 4 + t = 2.449489743 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 = 2.449489743 + -4 Combine like terms: 4 + -4 = 0 0 + t = 2.449489743 + -4 t = 2.449489743 + -4 Combine like terms: 2.449489743 + -4 = -1.550510257 t = -1.550510257 Simplifying t = -1.550510257Subproblem 2
t + 4 = -2.449489743 Simplifying t + 4 = -2.449489743 Reorder the terms: 4 + t = -2.449489743 Solving 4 + t = -2.449489743 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 = -2.449489743 + -4 Combine like terms: 4 + -4 = 0 0 + t = -2.449489743 + -4 t = -2.449489743 + -4 Combine like terms: -2.449489743 + -4 = -6.449489743 t = -6.449489743 Simplifying t = -6.449489743Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.550510257, -6.449489743}
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