X-√x+1=5

To solve the equation x-√x+1=5, we need to isolate the term with the square root.

Let's start by moving the term x to the right side of the equation:

√x+1 = x-5

Now, let's square both sides of the equation to eliminate the square root:

(√x+1)^2 = (x-5)^2

Expanding both sides:

x + 1 + 2√x + √x^2 = x^2 - 10x + 25

Simplifying:

√x^2 + 3√x - 10x + 2√x + 26 = x^2 - 10x + 25

Combining like terms:

x^2 + 3√x + 2√x - 10x + 10x - x^2 + 26 - 25 = 0

Simplifying further:

5√x + 1 = 0

Now, isolate the term with √x:

5√x = -1

Divide both sides by 5:

√x = -1/5

To solve for x, square both sides:

x = (-1/5)^2

x = 1/25

Therefore, the solution to the equation x-√x+1=5 is x = 1/25.