Solve the following quadratic equation for all values of x in simplest form. (x-4)^2=33

To solve for , we need to isolate it on one side of the equation.

Take the square root of both sides, making sure to use both positive and negative roots.

cannot be simplified, so we'll leave it as-is.

Add to both sides to fully isolate .

Expand the solution by making two solutions, one where is positive and one where it's negative.

Step-by-step explanation:

(x-4)^2=33

x^2-8x+16=33 subtract 33 from both sides

x^2-8x-17=0

Solve with quadratic formula

x=4±√33  or x=9.74456, x= -1.74456