How do you solve using the completing the square method x2+2x+4=0?

1 Answer
George C.
Apr 5, 2017

x=−1±√3i

Explanation:

Given:

x2+2x+4=0

Completing the square we get:

0=x2+2x+4

0=x2+2x+1+3

0=(x+1)2+3

Note that for any Real value of x, we have:

(x+1)2≥0

and so:

(x+1)2+3≥3

To solve this quadratic we need to use Complex numbers.

The difference of squares identity can be written:

a2−b2=(a−b)(a+b)

We use this with a=(x+1) and b=√3i as follows:

0=(x+1)2+3

0=(x+1)2−(√3i)2

0=((x+1)−√3i)((x+1)+√3i)

0=(x+1−√3i)(x+1+√3i)

Hence:

x=−1±√3i

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