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
