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