The solutions of the given quadratic equation are 3 + √2 and
3-√2.
What is completing the square method?
Completing the square method is one of the methods to find the roots of the given quadratic equation. In this method, we have to convert the given equation into a perfect square.
According to the given question
We have a quadratic equation
[tex]x^{2} +6x+9 = 2[/tex]
The solution of the above quadratic equation by completing the square method is given by
[tex]x^{2} + 6x + 9 = 2[/tex]
⇒[tex]x^{2} + 6x + 9 -2=0[/tex] (subtracting 2 from both the sides)
⇒[tex]x^{2} + 6x + 7= 0[/tex]
⇒[tex]x^{2} + 2(3x) + (3)^{2} -(3)^{2} +7=0[/tex]
⇒ [tex](x+3)^{2} -2= 0[/tex]
⇒[tex](x+3)^{2} =2[/tex]
⇒[tex](x+3) =[/tex] ±√2
⇒[tex]x =[/tex] 3 ±√2
⇒ x = 3 + √2 and x = 3-√2
Hence, the solutions of the given quadratic equation are 3 + √2 and
3-√2.
Thus, options C and D are correct.
Find out more information about completing the square method here:
https://brainly.com/question/26107616
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