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Simplifying 18t2 + -2t + -65 = 0 Reorder the terms: -65 + -2t + 18t2 = 0 Solving -65 + -2t + 18t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. -3.611111111 + -0.1111111111t + t2 = 0 Move the constant term to the right: Add '3.611111111' to each side of the equation. -3.611111111 + -0.1111111111t + 3.611111111 + t2 = 0 + 3.611111111 Reorder the terms: -3.611111111 + 3.611111111 + -0.1111111111t + t2 = 0 + 3.611111111 Combine like terms: -3.611111111 + 3.611111111 = 0.000000000 0.000000000 + -0.1111111111t + t2 = 0 + 3.611111111 -0.1111111111t + t2 = 0 + 3.611111111 Combine like terms: 0 + 3.611111111 = 3.611111111 -0.1111111111t + t2 = 3.611111111 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 = 3.611111111 + 0.003086419752 Reorder the terms: 0.003086419752 + -0.1111111111t + t2 = 3.611111111 + 0.003086419752 Combine like terms: 3.611111111 + 0.003086419752 = 3.614197530752 0.003086419752 + -0.1111111111t + t2 = 3.614197530752 Factor a perfect square on the left side: (t + -0.05555555555)(t + -0.05555555555) = 3.614197530752 Calculate the square root of the right side: 1.901104292 Break this problem into two subproblems by setting (t + -0.05555555555) equal to 1.901104292 and -1.901104292.Subproblem 1
t + -0.05555555555 = 1.901104292 Simplifying t + -0.05555555555 = 1.901104292 Reorder the terms: -0.05555555555 + t = 1.901104292 Solving -0.05555555555 + t = 1.901104292 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 = 1.901104292 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + t = 1.901104292 + 0.05555555555 t = 1.901104292 + 0.05555555555 Combine like terms: 1.901104292 + 0.05555555555 = 1.95665984755 t = 1.95665984755 Simplifying t = 1.95665984755Subproblem 2
t + -0.05555555555 = -1.901104292 Simplifying t + -0.05555555555 = -1.901104292 Reorder the terms: -0.05555555555 + t = -1.901104292 Solving -0.05555555555 + t = -1.901104292 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 = -1.901104292 + 0.05555555555 Combine like terms: -0.05555555555 + 0.05555555555 = 0.00000000000 0.00000000000 + t = -1.901104292 + 0.05555555555 t = -1.901104292 + 0.05555555555 Combine like terms: -1.901104292 + 0.05555555555 = -1.84554873645 t = -1.84554873645 Simplifying t = -1.84554873645Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.95665984755, -1.84554873645}
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