Solve x² + 12x + 6 = 0 using the completing-the-square method.

Solution:

Given x² + 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

x² + 12x + 6 + 36 = 0 + 36

x² + 12x + 36 = 36 - 6 = 30

x² + 2(x)(6) + 6² = (√30)²

This resembles a² + 2ab + b² = (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 x² + 12x + 6 = 0 is x = +√30 - 6 or -√30 - 6

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Solve x² + 12x + 6 = 0 using the completing-the-square method.

Summary:

By solving x² + 12x + 6 = 0 using the completing-the-square method, we got a solution as x = √30 - 6 or -√30 - 6.