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Simplifying -9t2 + -1t + 6 = 0 Reorder the terms: 6 + -1t + -9t2 = 0 Solving 6 + -1t + -9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. -0.6666666667 + 0.1111111111t + t2 = 0 Move the constant term to the right: Add '0.6666666667' to each side of the equation. -0.6666666667 + 0.1111111111t + 0.6666666667 + t2 = 0 + 0.6666666667 Reorder the terms: -0.6666666667 + 0.6666666667 + 0.1111111111t + t2 = 0 + 0.6666666667 Combine like terms: -0.6666666667 + 0.6666666667 = 0.0000000000 0.0000000000 + 0.1111111111t + t2 = 0 + 0.6666666667 0.1111111111t + t2 = 0 + 0.6666666667 Combine like terms: 0 + 0.6666666667 = 0.6666666667 0.1111111111t + t2 = 0.6666666667 The t term is 0.1111111111t. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111t + 0.003086419752 + t2 = 0.6666666667 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111t + t2 = 0.6666666667 + 0.003086419752 Combine like terms: 0.6666666667 + 0.003086419752 = 0.669753086452 0.003086419752 + 0.1111111111t + t2 = 0.669753086452 Factor a perfect square on the left side: (t + 0.05555555555)(t + 0.05555555555) = 0.669753086452 Calculate the square root of the right side: 0.818384437 Break this problem into two subproblems by setting (t + 0.05555555555) equal to 0.818384437 and -0.818384437.Subproblem 1
t + 0.05555555555 = 0.818384437 Simplifying t + 0.05555555555 = 0.818384437 Reorder the terms: 0.05555555555 + t = 0.818384437 Solving 0.05555555555 + t = 0.818384437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + t = 0.818384437 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + t = 0.818384437 + -0.05555555555 t = 0.818384437 + -0.05555555555 Combine like terms: 0.818384437 + -0.05555555555 = 0.76282888145 t = 0.76282888145 Simplifying t = 0.76282888145Subproblem 2
t + 0.05555555555 = -0.818384437 Simplifying t + 0.05555555555 = -0.818384437 Reorder the terms: 0.05555555555 + t = -0.818384437 Solving 0.05555555555 + t = -0.818384437 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + t = -0.818384437 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + t = -0.818384437 + -0.05555555555 t = -0.818384437 + -0.05555555555 Combine like terms: -0.818384437 + -0.05555555555 = -0.87393999255 t = -0.87393999255 Simplifying t = -0.87393999255Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.76282888145, -0.87393999255}
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