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

1 Answer
Feb 27, 2017

Answer:

#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)#