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# Solve x^{2} + 12x + 6 = 0 using the completing-the-square method.

**Solution:**

Given x^{2} + 12x + 6 = 0

The technique of completing the square means, we need to add a term which makes the equation a perfect square

The given equation resembles a quadratic equation, where a = 1, b = 12 and c = 6

The term that needs to be added is (-b/2)^{2}

(-12/2)^{2} = (-6)^{2} = 36

x^{2} + 12x + 6 + 36 = 0 + 36

x^{2} + 12x + 36 = 36 - 6 = 30

x^{2} + 2(x)(6) + 6^{2 }= (√30)^{2}

This resembles a^{2 }+ 2ab + b^{2} = (a + b)^{2}

(x + 6)^{2} = (√30)^{2}

Applying square-root on both sides, we get

x + 6 =±√30

x = +√30 - 6 or -√30 - 6

Therefore, the solution for x^{2} + 12x + 6 = 0 is x = +√30 - 6 or -√30 - 6

## Solve x^{2} + 12x + 6 = 0 using the completing-the-square method.

**Summary:**

By solving x^{2} + 12x + 6 = 0 using the completing-the-square method, we got a solution as x = √30 - 6 or -√30 - 6.

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