How do you solve using the completing the square method #x^2+4x-1=0#?

2 Answers
May 28, 2017

Answer:

#x=-2+-sqrt5#

Explanation:

#"to "color(blue)"complete the square"#

add #(1/2" coefficient of x-term")^2" to both sides"#

#"that is add " 1/2(4/2)^2=4" to both sides"#

#x^2+4x+color(red)(4)-1=0+color(red)(4)#

#rArr(x+2)^2-1=4#

#"add 1 to both sides"#

#rArr(x+2)^2=5#

#color(blue)"take the square root of both sides"#

#rArrx+2=+-sqrt5larr" note plus or minus"#

#rArrx=-2+-sqrt5#

May 28, 2017

Answer:

#x=-2+-sqrt5#

Explanation:

#x^2+4x-1=0#
#x^2+4x+(4/2)^2-(4/2)^2-1=0#
#(x+2)^2-5=0#
#(x+2)^2=5#
#x=-2+-sqrt5#