What should be added to both sides of the equation so that the left-hand side is a perfect square?

Question

43.What should be added to both sides of the equation so that the left-hand side is a perfect square? 

x² + 10x = 39

I had gotten the answer 13



Answer 1

x^2 + 10x = 39

Cut the middle coefficient of the linear term in half.

Then square it.

the middle coefficient of the linear term in bold above, is 10.

Half of that is 5

Squaring that is 25.

So you add 25 to both sides.

x^2 + 10x + 25 = 39 + 25

(x + 5 )(x + 5 ) = 64

(x+5)^2 = 64

x+5 = +- 8 <-- square root of both sides; must take positive and negative square root of 64

x = -5 +- 8

x = -5 + 8 or x = -5 - 8

x = 3 or x = -13