Question

Solve x2 + 10x = 24 by completing the square. Which is the solution set of the equation?

Answer 1

-12 and 2

Explanation:

`x^2+10x=24\\`

`x^2+2*5*x=24`

`x^2+2*5*x+5^2-5^2=24`

`(x^2+2*5*x+5^2)-5^2=24`

Using the identity

`a^2+2*a*b+b^2 = (a+b)^2`

we get

`(x+5)^2-5^2=24`

`(x+5)^2-25=24\\`

`(x+5)^2=24+25\\(x+5)^2=49\\(x+5)=+7 \\or (x+5)=-7\\`

Solving both of them we get

x=-12 or x=2