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Simplifying x^{2}+ 12x + 33 = 0 Reorder the terms: 33 + 12x + x^{2}= 0 Solving 33 + 12x + x^{2}= 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 12x + -33 + x^{2}= 0 + -33 Reorder the terms: 33 + -33 + 12x + x^{2}= 0 + -33 Combine like terms: 33 + -33 = 0 0 + 12x + x^{2}= 0 + -33 12x + x^{2}= 0 + -33 Combine like terms: 0 + -33 = -33 12x + x^{2}= -33 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x^{2}= -33 + 36 Reorder the terms: 36 + 12x + x^{2}= -33 + 36 Combine like terms: -33 + 36 = 3 36 + 12x + x^{2}= 3 Factor a perfect square on the left side: (x + 6)(x + 6) = 3 Calculate the square root of the right side: 1.732050808 Break this problem into two subproblems by setting (x + 6) equal to 1.732050808 and -1.732050808.## Subproblem 1

x + 6 = 1.732050808 Simplifying x + 6 = 1.732050808 Reorder the terms: 6 + x = 1.732050808 Solving 6 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 1.732050808 + -6 Combine like terms: 6 + -6 = 0 0 + x = 1.732050808 + -6 x = 1.732050808 + -6 Combine like terms: 1.732050808 + -6 = -4.267949192 x = -4.267949192 Simplifying x = -4.267949192## Subproblem 2

x + 6 = -1.732050808 Simplifying x + 6 = -1.732050808 Reorder the terms: 6 + x = -1.732050808 Solving 6 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -1.732050808 + -6 Combine like terms: 6 + -6 = 0 0 + x = -1.732050808 + -6 x = -1.732050808 + -6 Combine like terms: -1.732050808 + -6 = -7.732050808 x = -7.732050808 Simplifying x = -7.732050808## Solution

The solution to the problem is based on the solutions from the subproblems. x = {-4.267949192, -7.732050808}

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