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

1 Answer
George C.
Feb 27, 2017

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)

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