SOLUTION: I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why. (rad of 4-x PLUS the rad of x+6)

Question 849769: I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why.
(rad of 4-x PLUS the rad of x+6) all equal to 4
Found 2 solutions by stanbon, josgarithmetic:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
I have looked up this question on wolfram and mathway and they both give 3,-5, but the 3 as an extraneous solution, and I cannot figure out why.
(rad of 4-x PLUS the rad of x+6) all equal to 4
----------
sqrt(4-x) + sqrt(x+6) = 4
--------
Square both sides to get:
(4-x) + (x+6) + 2sqrt[(4-x)(x+6)] = 16
-----
2sqrt(-x^2-2x+24) = 6
----
sqrt(-x^2-2x+24) = 3
Square both sides to get:
-x^2-2x+24 = 9
---
x^2 + 2x - 15 = 0
----
Factor:
(x+5)(x-3) = 0
x = 3 or x = -5
----
Neither is extraneous.
Cheers,
Stan H.
======================
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Description: (rad of 4-x PLUS the rad of x+6) all equal to 4
can best be understood to mean: .

When you think you have finished finding the values for x, and you want to know if any is extraneous, you can check how the value works in the ORIGINAL equation.

CHECK -5.
?

TRUE!
.

CHECK 3.
?

TRUE.
.

BOTH solutions work in the original equation.
RELATED QUESTIONS
Please help me out on this equation: {{{ x^(2/3) = 16 }}} I got an answer, but they were... (answered by checkley77)
I know its -3 but I don't know if its extraneous or not. Find the solution of 5 radical (answered by Edwin McCravy)
ALRIGHT. SO THE PROBLEM IS WRITTEN AS FOLLOWS: {{{ 3*sqrt(-75)+5*sqrt(-48) }}} PERFORM... (answered by RAY100)
Hello! I've tried this website once and it really worked! So here's my question involving (answered by ewatrrr)
I don't know if i selected the right topic for this question. Translate point... (answered by Theo)
Hi I am stuck on this one which has me completely bamboozled. Your assistance would be... (answered by solver91311,stanbon)
How do I find the domain of f(x)= 9log(-x)+7? I have looked up how-to videos and they all (answered by Fombitz,math_helper)
My homework is online, this is the question it gave. Decide whether x=-2i, x=i are... (answered by jim_thompson5910)
I think I am doing this wrong because I got an answer 36 pi cm2. But my teacher marked it (answered by checkley79)