Solve for x
please show all workings​

Step-by-step explanation:

We want to solve the equation:

We can isolate the square root. Subtract x from both sides:

And square both sides:

Expand:

Isolate the equation:

Factor:

Zero Product Property:

Solve for each case. Hence:

Now, we need to check for extraneous solutions. To do so, we can substitute each value back into the original equation and check whether or not the resulting statement is true.

Testing x = -2/3:

Since the resulting statement is true, x = -2/3 is indeed a solution.

Testing x = 2:

Since the resulting statement is not true, x = 2 is not a solution.

Therefore, our only solution to the equation is x = -2/3.  

Step-by-step explanation:

Hey there!

Given;

Take "X" in right side.

Squaring on both sides;

Simplify;

Either;

3x+2 = 0

x= -2/3

Or;

x-2 = 0

x= 2

Check:

Keeping X= -2/3,

√(x²-4x+8 ) +X = 2-x

√{(-2/3)²-4*-2/3+8}+(-2/3) = 2+2/3

8/3 = 8/3 (True)

Now; Keeping X= 2

√{(2)²-4*2+8}+2 = 2-2

8 ≠0 (False)

Therefore, the value of X is -2/3.

Hope it helps!

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