Question

How do you solve the equation `x^2+4x=6` by completing the square?

Answer 1

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

Explanation:

First subtract `6` from both sides to get the quadratic equation into standard form:

`x^2+4x-6 = 0`

The difference of squares identity can be written:

`a^2-b^2 = (a-b)(a+b)`

Use this with `a=x+2` and `b=sqrt(10)` as follows:

`0 = x^2+4x-6`

`color(white)(0) = x^2+4x+4-10`

`color(white)(0) = (x+2)^2-(sqrt(10))^2`

`color(white)(0) = ((x+2)-sqrt(10))((x+2)+sqrt(10))`

`color(white)(0) = (x+2-sqrt(10))(x+2+sqrt(10))`

Hence:

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