How do you solve #x^2+10x-1=0# using completing the square?

1 Answer
Jun 15, 2015

Answer:

#x = -5+-sqrt(26)#

Explanation:

#x^2+10x-1 = 0#

simplify by moving the constant to the right side
#color(white)("XXXX")##x^2+10x = 1#

complete the square
#color(white)("XXXX")##x^2+10x+(10/2)^2 = 1 + (10/2)^2#

rewrite as a square and simplify the right side
#color(white)("XXXX")##(x+5)^2 = 26#

take the square root of both sides
#color(white)("XXXX")##x+5 = +-sqrt(26)#

subtract #5# from both sides to isolate #x#
#color(white)("XXXX")##x = -5+-sqrt(26)#