Given: A quadratic equation-
[tex]x^2-12x+11=0[/tex]Required: To solve the equation by completing the square method.
Explanation: The general form of a quadratic equation is-
[tex]ax^2+bx+c=0[/tex]The given equation can be solved by the method of completing the square by adding and subtracting the term-
[tex](\frac{b}{2})^2[/tex]Hence, the given equation can be written as-
[tex]x^2-12x+36-36+11=0[/tex]Now solving further as-
[tex]\begin{gathered} x^2-2\times6\times x+6^2-25=0 \\ (x-6)^2=25 \\ (x-6)=\sqrt{25} \\ (x-6)=\pm5 \end{gathered}[/tex]Thus,
[tex]\begin{gathered} x-6=5\text{ or } \\ x-6=-5 \end{gathered}[/tex]This gives-
[tex]\begin{gathered} x=11\text{ or} \\ x=1 \end{gathered}[/tex]Final Answer: The solution to the equation is x=11 or x=1.
