Question

Solve x^2 + 10x + 24 = 0 by completing the square
please help me

Answer 1

Half the middle number, and it's 'a', then (x+a)^2-b then square that number and put it outside where outside number is b
Then you get
\[ x^2 + 10x + 24 = 0 \\ \\ (x+5)^2-25+24 = 0 \\ \\ (x+5)^2-1=0\]

Answer 2

ok

Answer 3

a complete square has to be of the form: (px+q)^2

(px+q)(px+q) = (px)^2 +2pqx + q^2

when p=1 this reduces to: x^2 +2q x + q^2

we can see from this that we can solve for q from the middle term to find a suitable value to add to the equation in the form of q^2-q^2

2q = 10, when q = 5 ... therefore 5^2 - 5^2 can be added to the equation to complete a square