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

1 Answer
VNVDVI
Apr 1, 2018

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)

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