To solve by completing the square, you have to write the equation in the form x^2+2ax+a^2=(x+a)^2
Using 2ax=-8x, we can solve for a, which is 2ax/2x. We can then use this to find that a=-4.
Plug a=-4 into the equation x^2+2ax+a^2=(x+a)^2.
x^2-8x+(-4)^2=9+(-4)^2
x^2-8x+(-4)^2=25
Complete the square:
(x-4)^2=25
Solve x-4=sqrt25 (square root) and x-4=negsqrt25 (negative square root)
x=9 and x=-1.
These can be proven by plugging them into the above equation (x-4)^2=25.
9-4^2=25 and -1-4^2=25.
Hope this helps ;)
[tex] x^2 - 8x = 9 [/tex]
Add both sides the square of half of 8 , that is [tex] {(\frac{8}{2})} ^2 [/tex]
[tex] x^2 - 8x + (\frac{8}{2})^2 = 9 +(\frac{8}{2})^2
[/tex][tex] (x^2 -8x +4^2 ) = 9 +16 [/tex]
[tex] (x-4)^2 = 25 [/tex]
Take square root on both sides
[tex] x-4 = 5 [/tex] or [tex] x-4 = -5 [/tex]
⇒ x= 9 or x= -1
