What is the answer to x^2-2x+sqrt(2-x)=sqrt(2-x)+3 ?

The answer to x^2-2x+sqrt(2-x)=sqrt(2-x)+3 is x=-1,x=3

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x^2-2x+sqrt(2-x)=sqrt(2-x)+3

x^{2} - 2 x + 2 - x = 2 - x + 3

x = - 1, x = 3

Solution steps

x^{2} - 2 x + 2 - x = 2 - x + 3

Subtract

2 - x + 3

from both sides

x^{2} - 2 x + 2 - x - (2 - x + 3) = 2 - x + 3 - (2 - x + 3)

Simplify

x^{2} - 2 x - 3 = 0

Factor

x^{2} - 2 x - 3 : (x + 1) (x - 3)

(x + 1) (x - 3) = 0

Using the Zero Factor Principle:

ab = 0

then

a = 0

b = 0

x + 1 = 0 or x - 3 = 0

Solve

x + 1 = 0 : x = - 1

Solve

x - 3 = 0 : x = 3

x = - 1, x = 3

Verify Solutions:

x = - 1

True

, x = 3

True

The solutions are

x = - 1, x = 3

4 x - 32 - 16 = - 14

2 x = 10

4 + x = 2 x - 1

(2 x + 12)^{\frac{5}{4}} - 13 = 19

2 x - x^{2} = 1 - x

What is the answer to x^2-2x+sqrt(2-x)=sqrt(2-x)+3 ?
The answer to x^2-2x+sqrt(2-x)=sqrt(2-x)+3 is x=-1,x=3
Solve for x: x^2-2x+sqrt(2-x)=sqrt(2-x)+3
The solution is x=-1,x=3