SOLUTION: Solve for x: sqrt x-6 + sqrt x+6 = 6 a. 3 b. 16 c. 10 d. Cannot be solved This is what I have but it is not an answer. sqrt x-6 = sqrt x+6 +6 (sqrt x-6)^2 = (sq

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Solve for x: sqrt x-6 + sqrt x+6 = 6 a. 3 b. 16 c. 10 d. Cannot be solved This is what I have but it is not an answer. sqrt x-6 = sqrt x+6 +6 (sqrt x-6)^2 = (sq      Log On


   

Question 141322: Solve for x:
sqrt x-6 + sqrt x+6 = 6
a. 3
b. 16
c. 10
d. Cannot be solved
This is what I have but it is not an answer.
sqrt x-6 = sqrt x+6 +6
(sqrt x-6)^2 = (sqrt x+6+6)^2
(sqrt x+6)^2 + 2 * sqrt x+6*6+6^2
x+6 + 2 sqrt x+6 + 6 + 36
(sqrt x-6)^2 = (sqrt x+6+6)^2
x-6 = x + 6 + 2sqrt x+6+36
x-6 + x + 42 + 2sqrt x+6
2x - 6 = 2sqrt x+6
4x^2 + 36x - 36 + 4 (x+6)
4x^2 + 36x - 36 = 4x + 24
4x^2 - 32x = 0
4x(x - 8x) = 0
4x = 0 and x - 8 = 0
x = 0 x = 8
Found 2 solutions by oscargut, stanbon:
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
sqrt x-6 + sqrt x+6 = 6
This is what I have but it is not an answer.
sqrt x-6 = sqrt x+6 +6 (is wrong)
correct is: sqrt(x-6)=6-sqrt(x+6)
the procedure is good

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Solve for x:
sqrt (x-6) + sqrt (x+6) = 6
a. 3
b. 16
c. 10
d. Cannot be solved
This is what I have but it is not an answer.
sqrt x-6 = sqrt x+6 +6
-----------------
Your 2nd line should be:
sqrt(x-6) = 6 - sqrt(x+6)
Now square both sides to get:
x-6 = 36-12sqrt(x+6)+x+6
-12 = 36-12sqrt(x+6)
-1 = 3 - sqrt(x+6)
-4 = sqrt(x+6)
Square both sides to get:
16 = x+6
x = 10
Checking in sqrt (x-6) + sqrt (x+6) = 6 :
sqrt(4) + sqrt(16) = 6
2 + 4 = 6
6=6
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Cheers,
Stan H.



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