SOLUTION: solve for X by completeting the sqaure x^2 + 8x -4 = 0

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Question 1067493: solve for X by completeting the sqaure
x^2 + 8x -4 = 0


Found 2 solutions by Alan3354, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve for X by completeting the sqaure
x^2 + 8x -4 = 0
================
x^2 + 8x = 4
Complete the square.

Answer by ikleyn(53765) About Me  (Show Source):
You can put this solution on YOUR website!
.
solve for X by completeting the sqaure
x^2 + 8x -4 = 0
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

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

%28x%2B4%29%5E2 - 20 = 0

is equivalent to

%28x%2B4%29%5E2 = 20

is equivalent to

x+4 = +/- sqrt%2820%29

is equivalent to

x = -4+%2B-+sqrt%2820%29.


The two roots are x%5B1%5D = -4+%2B+2%2Asqrt%285%29  and  x%5B2%5D = -4+-+2%2Asqrt%285%29.

Solved.