## To solve the equation 4 - x = (x - 2)^2, we can start by expanding the right side using the formula (a - b)^2 = a^2 - 2ab + b^2.

(x - 2)^2 = x^2 - 4x + 4

Now our equation becomes:

4 - x = x^2 - 4x + 4

Next, let's move all terms to one side to form a quadratic equation:

x^2 - 4x + 4 - 4 + x - 4 = 0

Simplifying, we get:

x^2 - 3x - 4 = 0

Now we have a quadratic equation in the form of ax^2 + bx + c = 0, where a = 1, b = -3, and c = -4.

To solve this quadratic equation, we can either factorize it or use the quadratic formula:

1. Factoring method:

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

x - 4 = 0 or x + 1 = 0

x = 4 or x = -1

2. Quadratic formula:

x = (-b Â± âˆš(b^2 - 4ac)) / (2a)

x = (-(-3) Â± âˆš((-3)^2 - 4(1)(-4))) / (2(1))

x = (3 Â± âˆš(9 + 16)) / 2

x = (3 Â± âˆš25) / 2

x = (3 Â± 5) / 2

This gives us two solutions: x = 4 and x = -1.

So the solution to the equation 2 + âˆš(4 - x) = x is x = 4 and x = -1.