What is the solution to the equation #x^2 + 2x -165=0#?

1 Answer
George C.
Jan 4, 2016

#x = -1+-sqrt(166)#

Explanation:

Complete the square, then use the difference of squares identity, which can be written:

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

with #a = x+1# and #b = sqrt(166)# as follows:

#0 = x^2+2x-165#

#=x^2+2x+1-1-165#

#=(x+1)^2-166#

#=(x+1)^2-(sqrt(166))^2#

#=((x+1)-sqrt(166))((x+1)+sqrt(166))#

#=(x+1-sqrt(166))(x+1+sqrt(166))#

So the two roots are:

#x = -1-sqrt(166) ~~ -13.884#

#x = -1+sqrt(166) ~~ 11.884#

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