Question 160413: Given: square root of (10x+6)(-) square root of (4x+4) = 2
Solution:
1. I isolated sq rt. of (10+6) = 2 +sq.rt.(4x+4)
2. sq. rt. of (10x+6)^2 = {2 + (4x+4)}^2
3. get rid of sq. rt. 10x +6 = 4 + 4sq.rt.of (4x+4) + 4x+4
4. 10x +6 = 4x + 8 + sq.rt.(4x+4)mult.4
5. 6x -2 = sq.rt.(4x+4) mult.4
6. (6x-2)^2 = {sq. rt. (4x +4)mult. 4}^2
7. 36x^2 - 24x +4 = 16 (4x+4)
8. 36x^2 - 24x +4 = 64x + 64
9. 36x^2- 88x - 60= 0
After this I am having difficulty to come up with the solution. Where did I go wrong? Found 2 solutions by Earlsdon, scott8148:Answer by Earlsdon(6294) (Show Source):
You can put this solution on YOUR website! Have more faith in yourself!
What you have done so far is perfect!
Now you need to solve the quadratic equation which you can do by use of the quadratic formula:
In your equation, a = 36, b = -88, and c = -60, so make the appropriate substitutions to get: Simplify this. or or
Now as a final step, you should check these solutions by substition into the original eqation, and you may find that you have an "extraneous" solution which would have come from the act of squaring parts of the original equation.
I'll leave this as an exercise for the student!
(