X-√x+1=5

To solve the equation x - √(x + 1) = 5, we can follow these steps:

Step 1: Add √(x + 1) to both sides of the equation to isolate the x term on one side:

x - √(x + 1) + √(x + 1) = 5 + √(x + 1)

This simplifies to:

x = 5 + √(x + 1)

Step 2: Square both sides of the equation to eliminate the square root:

(x)^2 = (5 + √(x + 1))^2

This simplifies to:

x^2 = (5 + √(x + 1))^2

Step 3: Expand the right side of the equation:

x^2 = (5 + √(x + 1))(5 + √(x + 1))

This can be further simplified by using the FOIL method:

x^2 = 25 + 5√(x + 1) + 5√(x + 1) + (x + 1)

Simplifying further:

x^2 = 25 + 10√(x + 1) + x + 1

Step 4: Combine like terms on the right side:

x^2 = x + 26 + 10√(x + 1)

Step 5: Move all terms to one side to form a quadratic equation:

x^2 - x - 26 - 10√(x + 1) = 0

This is a quadratic equation in terms of x and √(x + 1).

At this point, you can use numerical or graphical methods to approximate the solution.

Alternatively, if you are allowed to use a calculator, you can graph both sides of the equation and find the intersection point(s) to solve for x.