CAn someone help me solve

[SQRT(4 - x)] - [SQRT(x + 6)] = 2

I answered the exact same question here

http://www.jiskha.com/display.cgi?id=1232543909

As drwls pointed out correctly at the end of the post I linked...

in my verification for x = -5
LS is indeed = to 2 so it clearly works.

the solution is
x = -5

X2_5x_14=0

To solve the equation [SQRT(4 - x)] - [SQRT(x + 6)] = 2, we need to isolate the variable x.

Step 1: Square both sides of the equation to get rid of the square roots:
([SQRT(4 - x)])^2 - 2[SQRT(4 - x)][SQRT(x + 6)] + ([SQRT(x + 6)])^2 = 2^2

Simplifying, we get:
4 - x - 2[SQRT(4 - x)][SQRT(x + 6)] + x + 6 = 4

Step 2: Simplify the equation:
[SQRT(4 - x)][SQRT(x + 6)] = 6

Step 3: Square both sides of the equation again to eliminate the square roots:
([SQRT(4 - x)][SQRT(x + 6)])^2 = 6^2

Simplifying, we get:
(4 - x)(x + 6) = 36

Step 4: Expand and simplify:
4x + 24 - x^2 - 6x = 36

Rearranging the terms, we get a quadratic equation:
-x^2 - 2x - 12 = 0

Step 5: Solve the quadratic equation. There are different methods to solve quadratic equations, such as factoring, completing the square, or using the quadratic formula.

Using the quadratic formula, x = (-b ± √(b^2 - 4ac)) / (2a), where a = -1, b = -2, and c = -12.

Plugging in the values, we get:
x = (-(-2) ± √((-2)^2 - 4(-1)(-12))) / (2(-1))
x = (2 ± √(4 - 48)) / (-2)
x = (2 ± √(-44)) / (-2)

Since we have a negative value inside the square root, we cannot find a real solution for x in this case. The equation has no real solutions.