How do you solve w224−w2+136=0 by completing the square?

1 Answer
JMicheli
Jul 18, 2016

The solutions will be w=6±4i.

Explanation:

We can start by removing fractions from the mix by multiplying both sides by 24:
w2−12w+52=0

Now observing that we need an equation looking like w+b where 2b=−12 it is clear that the squared term will be w−6.

Since (w−6)2=w2−12w+36 we can take 36 out of 52, this gives us:
(w−6)2+16=0

we can manipulate this:
(w−6)2=−16

And take the square root of both sides:
w−6=±4i
w=6±4i

You can check this answer by inputting the coefficients into the quadratic equation as well.

Related questions
See all questions in Completing the Square
Impact of this question
1934 views around the world
You can reuse this answer
Creative Commons License