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Simplifying t2 + 2t + -149 = 0 Reorder the terms: -149 + 2t + t2 = 0 Solving -149 + 2t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '149' to each side of the equation. -149 + 2t + 149 + t2 = 0 + 149 Reorder the terms: -149 + 149 + 2t + t2 = 0 + 149 Combine like terms: -149 + 149 = 0 0 + 2t + t2 = 0 + 149 2t + t2 = 0 + 149 Combine like terms: 0 + 149 = 149 2t + t2 = 149 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 = 149 + 1 Reorder the terms: 1 + 2t + t2 = 149 + 1 Combine like terms: 149 + 1 = 150 1 + 2t + t2 = 150 Factor a perfect square on the left side: (t + 1)(t + 1) = 150 Calculate the square root of the right side: 12.247448714 Break this problem into two subproblems by setting (t + 1) equal to 12.247448714 and -12.247448714.Subproblem 1
t + 1 = 12.247448714 Simplifying t + 1 = 12.247448714 Reorder the terms: 1 + t = 12.247448714 Solving 1 + t = 12.247448714 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 = 12.247448714 + -1 Combine like terms: 1 + -1 = 0 0 + t = 12.247448714 + -1 t = 12.247448714 + -1 Combine like terms: 12.247448714 + -1 = 11.247448714 t = 11.247448714 Simplifying t = 11.247448714Subproblem 2
t + 1 = -12.247448714 Simplifying t + 1 = -12.247448714 Reorder the terms: 1 + t = -12.247448714 Solving 1 + t = -12.247448714 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 = -12.247448714 + -1 Combine like terms: 1 + -1 = 0 0 + t = -12.247448714 + -1 t = -12.247448714 + -1 Combine like terms: -12.247448714 + -1 = -13.247448714 t = -13.247448714 Simplifying t = -13.247448714Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.247448714, -13.247448714}
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