Find all possible solutions. Give your answers in increasing order. Give your answers to the nearest thousandth. \[ \sqrt{-4 x+4}+5=8 x \] The smaller possible solution is Is it a solution? (yes or no) The larger possible solution is Is it a solution? (yes or no)

Step 1 ：Given the equation \(\sqrt{-4x+4}+5=8x\)

Step 2 ：Isolate the square root on one side of the equation to get \(\sqrt{-4x+4}=8x-5\)

Step 3 ：Square both sides of the equation to eliminate the square root, resulting in \(-4x+4=(8x-5)^2\)

Step 4 ：Solve the resulting quadratic equation to find the potential solutions for x, which are \(\frac{7}{16}\) and \(\frac{3}{4}\)

Step 5 ：Substitute these solutions back into the original equation to check if they are valid

Step 6 ：Neither \(\frac{7}{16}\) nor \(\frac{3}{4}\) make the original equation true, indicating that they are extraneous solutions

Step 7 ：\(\boxed{\text{Final Answer: There are no valid solutions to the given equation}}\)