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Simplifying t2 + 4t + -8 = 0 Reorder the terms: -8 + 4t + t2 = 0 Solving -8 + 4t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 4t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 4t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 4t + t2 = 0 + 8 4t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 4t + t2 = 8 The t term is 4t. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4t + 4 + t2 = 8 + 4 Reorder the terms: 4 + 4t + t2 = 8 + 4 Combine like terms: 8 + 4 = 12 4 + 4t + t2 = 12 Factor a perfect square on the left side: (t + 2)(t + 2) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + 2) equal to 3.464101615 and -3.464101615.Subproblem 1
t + 2 = 3.464101615 Simplifying t + 2 = 3.464101615 Reorder the terms: 2 + t = 3.464101615 Solving 2 + t = 3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = 3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + t = 3.464101615 + -2 t = 3.464101615 + -2 Combine like terms: 3.464101615 + -2 = 1.464101615 t = 1.464101615 Simplifying t = 1.464101615Subproblem 2
t + 2 = -3.464101615 Simplifying t + 2 = -3.464101615 Reorder the terms: 2 + t = -3.464101615 Solving 2 + t = -3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + t = -3.464101615 + -2 Combine like terms: 2 + -2 = 0 0 + t = -3.464101615 + -2 t = -3.464101615 + -2 Combine like terms: -3.464101615 + -2 = -5.464101615 t = -5.464101615 Simplifying t = -5.464101615Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.464101615, -5.464101615}
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