How to complete a square?

Question

I need some help on completing a square to solve a Quadratic Equations. Please explain every step in detail.

 

Examples

 

f²-12f-216=0

 

a²-18a+36=0

Answer 1

The form of the squared equation is x^2 + 2ax +a^2 = (x+a)^2 in this case 1 we have:

f2-12f-216=0, then, add 216 to both sides and we get f^2 -12f = 216 => the second term is 2*a*x so in this case a=12/2 = 6 to get the perfect square we need to add 36 to each side of the equal to obtain

f^2 -12f + 36= 216+36 This will lead us to (f-6)^2 = 252 => taking the square root in both sides we obtain that (f-6)=15.87. there are two answers x1 = -15.87 +6 =9.87; x2= 15.87+6=21.87

 

The second equation may be solved in the same way to obtain a1= 15.71and ;a2 = 3.71

and the equation is (a-9)^2 + 36=0 or (a-9)^2 = 45