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

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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

Pantelis K. A Level Maths tutor, GCSE Maths tutor, GCSE Physics tutor

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