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Simplifying 0 = 6t + -1(t * t) + 11 Multiply t * t 0 = 6t + -1(t2) + 11 Reorder the terms: 0 = 11 + 6t + -1t2 Solving 0 = 11 + 6t + -1t2 Solving for variable 't'. Combine like terms: 0 + -11 = -11 -11 + -6t + t2 = 11 + 6t + -1t2 + -11 + -6t + t2 Reorder the terms: -11 + -6t + t2 = 11 + -11 + 6t + -6t + -1t2 + t2 Combine like terms: 11 + -11 = 0 -11 + -6t + t2 = 0 + 6t + -6t + -1t2 + t2 -11 + -6t + t2 = 6t + -6t + -1t2 + t2 Combine like terms: 6t + -6t = 0 -11 + -6t + t2 = 0 + -1t2 + t2 -11 + -6t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 -11 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '11' to each side of the equation. -11 + -6t + 11 + t2 = 0 + 11 Reorder the terms: -11 + 11 + -6t + t2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -6t + t2 = 0 + 11 -6t + t2 = 0 + 11 Combine like terms: 0 + 11 = 11 -6t + t2 = 11 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 11 + 9 Reorder the terms: 9 + -6t + t2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + -6t + t2 = 20 Factor a perfect square on the left side: (t + -3)(t + -3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (t + -3) equal to 4.472135955 and -4.472135955.Subproblem 1
t + -3 = 4.472135955 Simplifying t + -3 = 4.472135955 Reorder the terms: -3 + t = 4.472135955 Solving -3 + t = 4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + t = 4.472135955 + 3 t = 4.472135955 + 3 Combine like terms: 4.472135955 + 3 = 7.472135955 t = 7.472135955 Simplifying t = 7.472135955Subproblem 2
t + -3 = -4.472135955 Simplifying t + -3 = -4.472135955 Reorder the terms: -3 + t = -4.472135955 Solving -3 + t = -4.472135955 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + t = -4.472135955 + 3 t = -4.472135955 + 3 Combine like terms: -4.472135955 + 3 = -1.472135955 t = -1.472135955 Simplifying t = -1.472135955Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.472135955, -1.472135955}
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