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Simplifying t2 + -1t + -8 = 0 Reorder the terms: -8 + -1t + t2 = 0 Solving -8 + -1t + 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 + -1t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + -1t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -1t + t2 = 0 + 8 -1t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 -1t + t2 = 8 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 8 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 8 + 0.25 Combine like terms: 8 + 0.25 = 8.25 0.25 + -1t + t2 = 8.25 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 8.25 Calculate the square root of the right side: 2.872281323 Break this problem into two subproblems by setting (t + -0.5) equal to 2.872281323 and -2.872281323.Subproblem 1
t + -0.5 = 2.872281323 Simplifying t + -0.5 = 2.872281323 Reorder the terms: -0.5 + t = 2.872281323 Solving -0.5 + t = 2.872281323 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 2.872281323 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 2.872281323 + 0.5 t = 2.872281323 + 0.5 Combine like terms: 2.872281323 + 0.5 = 3.372281323 t = 3.372281323 Simplifying t = 3.372281323Subproblem 2
t + -0.5 = -2.872281323 Simplifying t + -0.5 = -2.872281323 Reorder the terms: -0.5 + t = -2.872281323 Solving -0.5 + t = -2.872281323 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -2.872281323 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -2.872281323 + 0.5 t = -2.872281323 + 0.5 Combine like terms: -2.872281323 + 0.5 = -2.372281323 t = -2.372281323 Simplifying t = -2.372281323Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.372281323, -2.372281323}
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