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Simplifying 11 = x2 + -6x Reorder the terms: 11 = -6x + x2 Solving 11 = -6x + x2 Solving for variable 'x'. Reorder the terms: 11 + 6x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 11 + 6x + -1x2 = 0 + x2 + -1x2 11 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 11 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -11 + -6x + x2 = 0 Move the constant term to the right: Add '11' to each side of the equation. -11 + -6x + 11 + x2 = 0 + 11 Reorder the terms: -11 + 11 + -6x + x2 = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -6x + x2 = 0 + 11 -6x + x2 = 0 + 11 Combine like terms: 0 + 11 = 11 -6x + x2 = 11 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = 11 + 9 Reorder the terms: 9 + -6x + x2 = 11 + 9 Combine like terms: 11 + 9 = 20 9 + -6x + x2 = 20 Factor a perfect square on the left side: (x + -3)(x + -3) = 20 Calculate the square root of the right side: 4.472135955 Break this problem into two subproblems by setting (x + -3) equal to 4.472135955 and -4.472135955.Subproblem 1
x + -3 = 4.472135955 Simplifying x + -3 = 4.472135955 Reorder the terms: -3 + x = 4.472135955 Solving -3 + x = 4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + x = 4.472135955 + 3 x = 4.472135955 + 3 Combine like terms: 4.472135955 + 3 = 7.472135955 x = 7.472135955 Simplifying x = 7.472135955Subproblem 2
x + -3 = -4.472135955 Simplifying x + -3 = -4.472135955 Reorder the terms: -3 + x = -4.472135955 Solving -3 + x = -4.472135955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -4.472135955 + 3 Combine like terms: -3 + 3 = 0 0 + x = -4.472135955 + 3 x = -4.472135955 + 3 Combine like terms: -4.472135955 + 3 = -1.472135955 x = -1.472135955 Simplifying x = -1.472135955Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.472135955, -1.472135955}
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