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Simplifying 3t2 + 36t = 35 Reorder the terms: 36t + 3t2 = 35 Solving 36t + 3t2 = 35 Solving for variable 't'. Reorder the terms: -35 + 36t + 3t2 = 35 + -35 Combine like terms: 35 + -35 = 0 -35 + 36t + 3t2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -11.66666667 + 12t + t2 = 0 Move the constant term to the right: Add '11.66666667' to each side of the equation. -11.66666667 + 12t + 11.66666667 + t2 = 0 + 11.66666667 Reorder the terms: -11.66666667 + 11.66666667 + 12t + t2 = 0 + 11.66666667 Combine like terms: -11.66666667 + 11.66666667 = 0.00000000 0.00000000 + 12t + t2 = 0 + 11.66666667 12t + t2 = 0 + 11.66666667 Combine like terms: 0 + 11.66666667 = 11.66666667 12t + t2 = 11.66666667 The t term is 12t. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12t + 36 + t2 = 11.66666667 + 36 Reorder the terms: 36 + 12t + t2 = 11.66666667 + 36 Combine like terms: 11.66666667 + 36 = 47.66666667 36 + 12t + t2 = 47.66666667 Factor a perfect square on the left side: (t + 6)(t + 6) = 47.66666667 Calculate the square root of the right side: 6.904105059 Break this problem into two subproblems by setting (t + 6) equal to 6.904105059 and -6.904105059.Subproblem 1
t + 6 = 6.904105059 Simplifying t + 6 = 6.904105059 Reorder the terms: 6 + t = 6.904105059 Solving 6 + t = 6.904105059 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = 6.904105059 + -6 Combine like terms: 6 + -6 = 0 0 + t = 6.904105059 + -6 t = 6.904105059 + -6 Combine like terms: 6.904105059 + -6 = 0.904105059 t = 0.904105059 Simplifying t = 0.904105059Subproblem 2
t + 6 = -6.904105059 Simplifying t + 6 = -6.904105059 Reorder the terms: 6 + t = -6.904105059 Solving 6 + t = -6.904105059 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = -6.904105059 + -6 Combine like terms: 6 + -6 = 0 0 + t = -6.904105059 + -6 t = -6.904105059 + -6 Combine like terms: -6.904105059 + -6 = -12.904105059 t = -12.904105059 Simplifying t = -12.904105059Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.904105059, -12.904105059}
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