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

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Answer 1 · 2016-05-28T17:06:53

The solutions are:
#color(green)(x = 3sqrt 3 - 5# ,# color(green)(x = -3sqrt 3 -5 #

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

#x^2 +10x = 2 #

To write the Left Hand Side as a Perfect Square, we add 25 to both sides:

#x^2 +10x + color(blue)(25)= 2 + color(blue)(25) #

#x^2 + 2 * x * 5 + 5^2 = 27#

Using the Identity #color(blue)((a+b)^2 = a^2 + 2ab + b^2#, we get

#(x+5)^2 = 27#

#x + 5 = sqrt27# or #x +5 = -sqrt27#

(Note: prime factorising #27; 27 = 3 * 3 * 3 = 3^3

So, #sqrt27 = sqrt (3^3) = 3sqrt3# )

#x + 5 = 3sqrt3# or #x +5 = -3sqrt3#

#color(green)(x = 3sqrt 3 - 5# ,# color(green)(x = -3sqrt 3 -5 #