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Simplifying 12t2 + 9t = 1 Reorder the terms: 9t + 12t2 = 1 Solving 9t + 12t2 = 1 Solving for variable 't'. Reorder the terms: -1 + 9t + 12t2 = 1 + -1 Combine like terms: 1 + -1 = 0 -1 + 9t + 12t2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. -0.08333333333 + 0.75t + t2 = 0 Move the constant term to the right: Add '0.08333333333' to each side of the equation. -0.08333333333 + 0.75t + 0.08333333333 + t2 = 0 + 0.08333333333 Reorder the terms: -0.08333333333 + 0.08333333333 + 0.75t + t2 = 0 + 0.08333333333 Combine like terms: -0.08333333333 + 0.08333333333 = 0.00000000000 0.00000000000 + 0.75t + t2 = 0 + 0.08333333333 0.75t + t2 = 0 + 0.08333333333 Combine like terms: 0 + 0.08333333333 = 0.08333333333 0.75t + t2 = 0.08333333333 The t term is 0.75t. Take half its coefficient (0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. 0.75t + 0.140625 + t2 = 0.08333333333 + 0.140625 Reorder the terms: 0.140625 + 0.75t + t2 = 0.08333333333 + 0.140625 Combine like terms: 0.08333333333 + 0.140625 = 0.22395833333 0.140625 + 0.75t + t2 = 0.22395833333 Factor a perfect square on the left side: (t + 0.375)(t + 0.375) = 0.22395833333 Calculate the square root of the right side: 0.473242362 Break this problem into two subproblems by setting (t + 0.375) equal to 0.473242362 and -0.473242362.Subproblem 1
t + 0.375 = 0.473242362 Simplifying t + 0.375 = 0.473242362 Reorder the terms: 0.375 + t = 0.473242362 Solving 0.375 + t = 0.473242362 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = 0.473242362 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = 0.473242362 + -0.375 t = 0.473242362 + -0.375 Combine like terms: 0.473242362 + -0.375 = 0.098242362 t = 0.098242362 Simplifying t = 0.098242362Subproblem 2
t + 0.375 = -0.473242362 Simplifying t + 0.375 = -0.473242362 Reorder the terms: 0.375 + t = -0.473242362 Solving 0.375 + t = -0.473242362 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.375' to each side of the equation. 0.375 + -0.375 + t = -0.473242362 + -0.375 Combine like terms: 0.375 + -0.375 = 0.000 0.000 + t = -0.473242362 + -0.375 t = -0.473242362 + -0.375 Combine like terms: -0.473242362 + -0.375 = -0.848242362 t = -0.848242362 Simplifying t = -0.848242362Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.098242362, -0.848242362}
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