Completing the Square

Question

x^2+x=14

Solve by completing the square

Answer 1

The first thing we need to do is divide the power-1 x term by two, and then square it.

1 / 2 = .5

.5² = .25

 

So we now have:

x² + x + .25 - .25 = 14 (if we add in .25, we need to subtract it as well to keep it evenly)

x² + x + .25 = 14.25

 

Now to factor out into our square format:

(x + .5)² = 14.25 (that .5 comes from the halving we did at the start)

 

x + .5 = ± √14.25

x = -.5 ± √14.25