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Simplifying (x + 3)(x + 3) = 11 Reorder the terms: (3 + x)(x + 3) = 11 Reorder the terms: (3 + x)(3 + x) = 11 Multiply (3 + x) * (3 + x) (3(3 + x) + x(3 + x)) = 11 ((3 * 3 + x * 3) + x(3 + x)) = 11 ((9 + 3x) + x(3 + x)) = 11 (9 + 3x + (3 * x + x * x)) = 11 (9 + 3x + (3x + x2)) = 11 Combine like terms: 3x + 3x = 6x (9 + 6x + x2) = 11 Solving 9 + 6x + x2 = 11 Solving for variable 'x'. Reorder the terms: 9 + -11 + 6x + x2 = 11 + -11 Combine like terms: 9 + -11 = -2 -2 + 6x + x2 = 11 + -11 Combine like terms: 11 + -11 = 0 -2 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + 6x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 6x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 6x + x2 = 0 + 2 6x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 6x + x2 = 2 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 = 2 + 9 Reorder the terms: 9 + 6x + x2 = 2 + 9 Combine like terms: 2 + 9 = 11 9 + 6x + x2 = 11 Factor a perfect square on the left side: (x + 3)(x + 3) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 3) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 3 = 3.31662479 Simplifying x + 3 = 3.31662479 Reorder the terms: 3 + x = 3.31662479 Solving 3 + x = 3.31662479 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 = 3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = 3.31662479 + -3 x = 3.31662479 + -3 Combine like terms: 3.31662479 + -3 = 0.31662479 x = 0.31662479 Simplifying x = 0.31662479Subproblem 2
x + 3 = -3.31662479 Simplifying x + 3 = -3.31662479 Reorder the terms: 3 + x = -3.31662479 Solving 3 + x = -3.31662479 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 = -3.31662479 + -3 Combine like terms: 3 + -3 = 0 0 + x = -3.31662479 + -3 x = -3.31662479 + -3 Combine like terms: -3.31662479 + -3 = -6.31662479 x = -6.31662479 Simplifying x = -6.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31662479, -6.31662479}
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