SOLUTION: Hello, I've been trying to solve this equation but it seems I can only get down to simplifying it. Please help =) SOLVE THE EQUATION SYMBOLICALLY sqrt(x+6) + sqrt(2-x) = 4

Question 85463: Hello, I've been trying to solve this equation but it seems I can only get down to simplifying it. Please help =)
SOLVE THE EQUATION SYMBOLICALLY
sqrt(x+6) + sqrt(2-x) = 4
Found 3 solutions by jim_thompson5910, scianci, Earlsdon:
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
Start with the given equation

Subtract from both sides

Square both sides

FOIL the right side

Get everything but the term to the left side

Combine like terms on the left side

Square both sides

FOIL the left side

Distribute

Get everything to one side

Factor out a 4

Factor the expression in the parenthesis

So we have an answer of

Check:
Plug in

solution works

Answer by scianci(186)   (Show Source): You can put this solution on YOUR website!
Isolate the radicals by subtracting one of them from both sides:
= 4 -
Square both sides:
= (4 - )^2
x + 6 = 16 - 8 + 2-x
x + 6 = 18 - 8-x
Isolate the remaining radical:
x + x + 6 - 18 = - 8
2x-12 = - 8
Square both sides again:
= (- 8)^2
- 48x + 144 = 64(2 - x)
-48x+144 = 128-64x
+16x+16 = 0
+ 4x + 4 = 0
(x + 2)(x + 2) = 0
x + 2 = 0
x = -2 [potentially]
Check for extraneous solutions:
= 4 - ?
= 4 - ?
2 = 4 - 2 ?
2 = 2 ; OK
x = -2 is a valid solution
Answer by Earlsdon(6294)   (Show Source): You can put this solution on YOUR website!
Solve:
First, separate the square roots. Subtract from both sides.
Next, square both sides.
Simplify so that you have only the radical (or a multiple thereof) on one side.
Add x to both sides.
Subtract 18 from both sides.
Now square both sides again.
Simplify this so that you have a quadratic equation in standard form.
Add 64x to both sides.
Subtract 128 from both sides.
Factor out a 4 to simplify this.
Now factor the parentheses.
Applying the zero products principle, you get the double root:

Check:
Set x = -2.
Simplify.

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