Question

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

Answer 1

Answer:

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

Answer 2

$\huge\text{ x=\boxed{\sqrt{33}+4,\ -\sqrt{33}+4} }$

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.

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

$\sqrt{33}$ cannot be simplified, so we'll leave it as-is.

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

$x=\pm\sqrt{33}+4$

Expand the solution by making two solutions, one where $\sqrt{33}$ is positive and one where it's negative.

$x=\sqrt{33}+4,\ x=-\sqrt{33}+4\\x=\boxed{\sqrt{33}+4,\ -\sqrt{33}+4}$