Question 1067493
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solve for X by completeting the sqaure

   x^2 + 8x -4 = 0
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x^2 + 8x - 4 = 0.


You have these two terms x^2 + 8x . . . 
So, the thought which comes first to your mind is to get (x+4)^2.
To bring it to reality, you need to add 4^2 = 16 and to distract it to keep the balance.
Now, see how I do it below:


x^2 + 8x - 4 = 0

is equivalent to

(x^2 + 8x + 16) - 16 - 4 = 0

is equivalent to

{{{(x+4)^2}}} - 20 = 0

is equivalent to

{{{(x+4)^2}}} = 20

is equivalent to

x+4 = +/- {{{sqrt(20)}}}

is equivalent to

x = {{{-4 +- sqrt(20)}}}.


The two roots are {{{x[1]}}} = {{{-4 + 2*sqrt(5)}}}  and  {{{x[2]}}} = {{{-4 - 2*sqrt(5)}}}.
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Solved.