Question

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

Answer 1

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

Answer 2

`\huge\text{$x=\boxed{√(33)+4,\ -√(33)+4}$}`

To solve for
`x`, 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.

`\begin{aligned}(x-4)^2&=33\\x-4&=\pm√(33)\end{aligned}`

`√(33)` cannot be simplified, so we'll leave it as-is.

Add
`4` to both sides to fully isolate
`x`.

`x=\pm√(33)+4`

Expand the solution by making two solutions, one where
`√(33)` is positive and one where it's negative.

`x=√(33)+4,\ x=-√(33)+4\\x=\boxed{√(33)+4,\ -√(33)+4}`