SOLUTION: Solve by completing the square. x^2-6x-4=0

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Solve by completing the square. x^2-6x-4=0      Log On


   

Question 969850: Solve by completing the square. x^2-6x-4=0
Found 2 solutions by erica65404, josmiceli:
Answer by erica65404(394) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2-6x-4=0
The first thing you want to do when completing the square is find b.
ax%5E2%2Bbx%2Bc=0 can be used to find b in a trinomial.
when you look at the equation you were given you can see that b = -6.
now take the absolute value of b which would be 6 and divide it by 2.
This gives you 3.
Then square this number.
This gives you 9.
add 9 to each side of the equation
x%5E2-6x%2B9-4=0%2B9
This part of the equation x%5E2-6x%2B9 can be factored into %28x-3%29%28x-3%29
This is the same as %28x-3%29%5E2.
now you have the equation %28x-3%29%5E2+-4=9
Solve for x
%28x-3%29%5E2+-4=9
%28x-3%29%5E2=13
x-3+=+%2B-+sqrt%2813%29
x=+3+%2B-+sqrt%2813%29
The answers are x=+3+%2B+sqrt%2813%29 and x=+3+-+sqrt%2813%29

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
+x%5E2++-+6x+-+4+=+0+
Add +4+ to both sides
+x%5E2++-+6x+=+4+
Take +1%2F2+ of the coefficient of The
+x+ term, square it, and add it to both sides
----------------------------
+x%5E2+-+6x+%2B+%28+-6%2F2+%29%5E2+=+4+%2B+%28+-6%2F2+%29%5E2+
+x%5E2+-+6x+%2B+9+=+4+%2B+9+
+x%5E2+-+6x+%2B+9+=+13+
+%28+x+-+3+%29%5E2+=+13+
Take the square root of both sides
+x+-+3+=+sqrt%2813%29+
+x+=+3+%2B+sqrt%2813%29+
And also, taking the negative square root,
+x+=+3+-+sqrt%2813%29+
---------------------
check answer:
+x%5E2++-+6x+-+4+=+0+
+%28+3+-+sqrt%2813%29+%29%5E2+-+6%2A%28+3+-+sqrt%2813%29+%29++-+4+=+0+
+9+-+6%2Asqrt%2813%29+%2B+13+-+18+%2B+6%2Asqrt%2813%29+-+4+=+0+
+9+%2B+13+-+18+-+4+=+0+
+22+-+22+=+0+
OK
You can check +x+=+3+%2B+sqrt%2813%29+