To solve the given quadratic equation [tex]\( x^2 + 6x - 6 = 0 \)[/tex] by completing the square, follow these detailed steps:
1. Move the constant term to the right side of the equation:
[tex]\[ x^2 + 6x - 6 = 0 \][/tex]
[tex]\[ x^2 + 6x = 6 \][/tex]
2. Complete the square:
To complete the square, you need to take the coefficient of [tex]\( x \)[/tex] (which is 6), divide it by 2, and then square the result.
[tex]\[ \left( \frac{6}{2} \right)^2 = 3^2 = 9 \][/tex]
Add and subtract this square (9) within the left-hand side of the equation:
[tex]\[ x^2 + 6x + 9 - 9 = 6 \][/tex]
[tex]\[ (x + 3)^2 - 9 = 6 \][/tex]
3. Move the -9 term to the right side to complete the square:
[tex]\[ (x + 3)^2 - 9 = 6 \][/tex]
[tex]\[ (x + 3)^2 = 6 + 9 \][/tex]
[tex]\[ (x + 3)^2 = 15 \][/tex]
Thus, the equation [tex]\( x^2 + 6x - 6 = 0 \)[/tex] rewritten by completing the square is:
[tex]\[ (x + 3)^2 = 15 \][/tex]
So, the correct answer is:
A. [tex]\((x+3)^2=15\)[/tex]
