How do you solve using the completing the square method #x^2 + 4x = 6#?

1 Answer
Apr 1, 2018

Answer:

#x=-2+-sqrt(10)#

Explanation:

When wanting to complete the square for a quadratic in the form

#ax^2+bx=c#, we add #(b/2)^2# to each side and factor the left side. To solve, we can take the root of both sides, accounting for positive and negative answers on the right side.

In this case, #b=4, (b/2)^2=(4/2)^2=2^2=4#, so we add #4# to each side.

#x^4+4x+4=6+4#

Factoring #x^4+4x+4# yields #(x+2)^2#

#(x+2)^2=10#

So, take the root of both sides, account for positive and negative:

#sqrt((x+2)^2)=+-sqrt(10)#

The root of a squared term is just that term:

#x+2=+-sqrt(10)#

#x=-2+-sqrt(10)#