Find the roots of the quadratic equation, x^2 - 8x + 24 = 0, by completing the square.

Step 1:

The fisrt step is to use the following formula when asked to complete the square,

( x + (b/2) )² - (b/2)² + c = 0

Step 2

In our case, b=8,c=24

Hence our equation,

x² - 8x + 24= 0

becomes 

(x + (-8/2) )² - (-8/2)² + 24 = 0

which is equal to

(x - 4 )² - (4)² + 24 = 0

(x - 4 )² - 16 + 24 = 0

(x - 4 )² + 8 = 0

Step 3:

Now we take 8 to the RHS, as this will allow us to take the square root of both sides.

(x - 4 )² = -8

(x - 4 ) = +/- (-8)^1/2

x = 4 +/- (-8)^1/2

Hence the roots of x² - 8x + 24= 0 are

x = 4 + (-8)^1/2  and x = 4 - (-8)^1/2