How do you solve using completing the square method #x^2+5x-2=0#?

1 Answer
Oct 30, 2017

Answer:

#x = -5/2+-sqrt(33)/2#

Explanation:

The difference of square identity can be written:

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

Use this with #a=(2x+5)# and #b=sqrt(33)#

First premultiply by #4# to reduce the amount of fraction arithmetic we need to do...

#0 = 4(x^2+5x-2)#

#color(white)(0) = 4x^2+20x-8#

#color(white)(0) = (2x)^2+2(2x)(5)+5^2-33#

#color(white)(0) = (2x+5)^2-(sqrt(33))^2#

#color(white)(0) = ((2x+5)-sqrt(33))((2x+5)+sqrt(33))#

#color(white)(0) = (2x+5-sqrt(33))(2x+5+sqrt(33))#

So:

#2x = -5+-sqrt(33)#

So:

#x = -5/2+-sqrt(33)/2#