\( 1.24-x=\sqrt{x-4} \)

To solve the equation \( 1.24 - x = \sqrt{x - 4} \), we first isolate the square root. Rearranging gives us \( \sqrt{x - 4} = 1.24 - x \). Now, to eliminate the square root, we square both sides, resulting in \( x - 4 = (1.24 - x)^2 \). Expanding the right side yields \( x - 4 = 1.5376 - 2.48x + x^2 \). Now, rearranging all terms to one side leads to the quadratic equation \( x^2 - 3.48x + 5.5376 = 0 \). Using the quadratic formula, we find the values of \( x \). With a little calculation, we get \( x \approx 3.1691 \) or \( x \approx 1.7009 \). However, we need to check which of these solutions satisfies the original equation, particularly since squaring can introduce extraneous solutions. Plugging \( x = 3.1691 \) back into the original equation shows it is a valid solution, while \( x = 1.7009 \) does not satisfy it. So, the solution to the equation is \( x \approx 3.1691 \).