√x + 1/2 = √5/2

To solve the equation, we need to isolate the variable x.

First, let's subtract 1/2 from both sides of the equation:

√x + 1/2 - 1/2 = √5/2 - 1/2

Simplifying, we have:

√x = √5/2 - 1/2

Next, let's simplify the right side of the equation:

√x = (√5 - 1)/2

To eliminate the square root, we can square both sides of the equation:

(√x)^2 = (√5 - 1)^2/2^2

Simplifying further, we have:

x = (5 - 2√5 + 1)/4

Combining like terms, we get:

x = (6 - 2√5)/4

Finally, we can simplify the expression:

x = 3/2 - √5/2