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Simplifying x^{2}+ 12x = 33 Reorder the terms: 12x + x^{2}= 33 Solving 12x + x^{2}= 33 Solving for variable 'x'. Reorder the terms: -33 + 12x + x^{2}= 33 + -33 Combine like terms: 33 + -33 = 0 -33 + 12x + x^{2}= 0 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 = 69 36 + 12x + x^{2}= 69 Factor a perfect square on the left side: (x + 6)(x + 6) = 69 Calculate the square root of the right side: 8.306623863 Break this problem into two subproblems by setting (x + 6) equal to 8.306623863 and -8.306623863.## Subproblem 1

x + 6 = 8.306623863 Simplifying x + 6 = 8.306623863 Reorder the terms: 6 + x = 8.306623863 Solving 6 + x = 8.306623863 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 = 8.306623863 + -6 Combine like terms: 6 + -6 = 0 0 + x = 8.306623863 + -6 x = 8.306623863 + -6 Combine like terms: 8.306623863 + -6 = 2.306623863 x = 2.306623863 Simplifying x = 2.306623863## Subproblem 2

x + 6 = -8.306623863 Simplifying x + 6 = -8.306623863 Reorder the terms: 6 + x = -8.306623863 Solving 6 + x = -8.306623863 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 = -8.306623863 + -6 Combine like terms: 6 + -6 = 0 0 + x = -8.306623863 + -6 x = -8.306623863 + -6 Combine like terms: -8.306623863 + -6 = -14.306623863 x = -14.306623863 Simplifying x = -14.306623863## Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.306623863, -14.306623863}

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