SOLUTION: I am trying to solve the following: x2 -4x -3 = 0. I can get as far as 4 plus or minus the sqrt of 28 over 2. I don't understand why this becomes 2 plus or minus the sqrt of 7.

Question 308520: I am trying to solve the following: x2 -4x -3 = 0. I can get as far as 4 plus or minus the sqrt of 28 over 2. I don't understand why this becomes 2 plus or minus the sqrt of 7. It seems to me that it should be 2 plus or minus the sqrt of 14.
Thanks. Marieann
Found 3 solutions by ankor@dixie-net.com, stanbon, mananth:
Answer by ankor@dixie-net.com(22740)   (Show Source): You can put this solution on YOUR website!
solve the following: x^2 - 4x - 3 = 0
:
We can solve this by completing the square
x^2 - 4x + ___ = 3
:
x^2 - 4x + 4 = 3 + 4
:
(x-2)^2 = 7
:
x - 2 = +/-
Two solutions
x = 2 +
and
x = 2 -
Answer by stanbon(75887)   (Show Source): You can put this solution on YOUR website!
I am trying to solve the following: x^2 -4x -3 = 0. I can get as far as 4 plus or minus the sqrt of 28 over 2. I don't understand why this becomes 2 plus or minus the sqrt of 7. It seems to me that it should be 2 plus or minus the sqrt of 14.
------------------------------------------
Quadratic Formula:
x = [-b +- sqrt(b^2-4ac)]/(2a)
---
x = [4 +- sqrt(4^2 - 4*1*-3)]/(2*1)
---
x = [4 +- sqrt(28)]/2
---
x = [4 +- 2sqrt(7)]/2
---
x = [2+sqrt(7)] or x = [2-sqrt(7)]
====================================
Cheers,
Stan H.
====================================
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
I am trying to solve the following: x2 -4x -3 = 0. I can get as far as 4 plus or minus the sqrt of 28 over 2. I don't understand why this becomes 2 plus or minus the sqrt of 7. It seems to me that it should be 2 plus or minus the sqrt of 14.
x^2-4x-3
a=1 b=-4 c=-3
root x1 = -(-4)+sqrt((-4)^2-4*1*-3 /2
x1= 4 + sqrt (16+12) /2
x1 = 4 + sqrt28 /2
x1= (4 + sqrt( 2*2*7 ))/2
x1= (4+ sqrt4*sqrt7)/2
x1= (4+2sqrt7)/ 2
Similarly for x2
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