Question

Find the roots of the quadratic equation x^2 – 8x = 9 by completing the square. Show your work

Answer 1

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 ;)

Answer 2

`x^2 - 8x = 9`

Add both sides the square of half of 8 , that is
`{((8)/(2))} ^2`

`image`
`(x^2 -8x +4^2 ) = 9 +16`

`(x-4)^2 = 25`

Take square root on both sides

`x-4 = 5` or
`x-4 = -5`

⇒ x= 9 or x= -1