Answer:
[tex]\large\boxed{\red{\sf x =6+\sqrt{53},6-\sqrt{53}} }[/tex]
Step-by-step explanation:
We would like to solve the given quadratic equation by completing the square method .The given equation is ;
[tex]\longrightarrow x^2=12x +17[/tex]
Subtract 12x to both sides ,
[tex]\longrightarrow x^2-12x = 17 [/tex]
Here the co-efficient of x² is already 1 . So , we shall rewrite it as ,
[tex]\longrightarrow x^2-2(6)(x) = 17 [/tex]
Add 6² on both sides ,
[tex]\longrightarrow x^2-2(6)(x) + 6^2=17+6^2 [/tex]
Now LHS is in the form of (a-b)² = a²-2ab+b² ; so that ;
[tex]\longrightarrow (x -6)^2 = 17+36 [/tex]
Simplify RHS ,
[tex]\longrightarrow (x-6)^2=53 [/tex]
Put square root on both sides,
[tex]\longrightarrow (x-6) = \pm\sqrt{53}[/tex]
Add 6 on both sides,
[tex]\longrightarrow x = 6\pm\sqrt{53} [/tex]
Separate the two solutions ,
[tex]\longrightarrow \underline{\underline{x =6+\sqrt{53},6-\sqrt{53}}} [/tex]
And we are done!
