Can anyone help me solve for x?

Question

sqrt(5-x)+1=x-2

Can anyone help me solve for x or at least tell me how to do the steps?!
Thank you!

Answer 1

√(5 - x)+1=x - 2.

Subtract 1 from each side.

√(5 - x) = x - 3.

Take square each side.

[√(5 - x)]² = [x - 3]².

(5 - x) = x² - 6x + 9

Subtract (5 - x) from each side.

x² - 5x + 4 = 0

Now slove the equation using factor method.

x² - 4x - x + 4 = 0

x(x - 4) -1(x - 4) = 0

Take out common factors.

(x - 4)(x - 1) = 0

x - 4 = 0 or x -1 = 0

x - 4 = 0 then x = 4.

x - 1 = 0 then x = 1.

So, x = 1 or  4.

Comments

Check :

Substitute the value x = 1 in original equation : √(5 - x) + 1 = x - 2.

√(5 - 1) + 1 = 1 - 2

√(4) + 1 = - 1

2 + 1 = - 1

3 = - 1.

The above statement is false.

So, x = 1 is not a solution of √(5 - x) + 1 = x - 2.

 

Substitute the value x = 4 in original equation : √(5 - x) + 1 = x - 2.

√(5 - 4) + 1 = 4 - 2

√(1) + 1 = 2

1 + 1 = 2

2 = 2.

The above statement is true.

So, x = 4 is a solution of √(5 - x) + 1 = x - 2.

 

Therefore, the solution of √(5 - x) + 1 = x - 2 is x = 4.