Question

PLEASE HELP ME NOW!!

Answer 1

Hello!

The answer is:

The correct answer is the first option.

$(x-4)^{2}=4+-2\sqrt{7}$

Why?

To solve the problem, we must remember the following square root property:

$\sqrt{ab}=\sqrt{a}\sqrt{b}$

So,

We are given the expression:

$(x-4)^{2}=28$

Now, isolating we have:

First, applying square root to both sides of the equation in order to simplify the quadratic term, we have:

$\sqrt{(x-4)^{2} }=\sqrt{28}\\(x-4)=\sqrt{4*7}\\\\x=4+-(\sqrt{4}*\sqrt{7})\\\\x=4+-2\sqrt{7}$

Hence, the correct answer is the first option.

$(x-4)^{2}=4+-2\sqrt{7}$

Have a nice day!

Answer 2

Answer:

$x=4+-2\sqrt{7}$

Step-by-step explanation:

To solve, we need to take square root of both sides first:

$(x-4)^2=28\\\sqrt{(x-4)^2} =+-\sqrt{28} \\x-4=+-\sqrt{28}$

Now we use the property of radical shown below to simplify square root of 28:

Property:  $\sqrt{x*y}=\sqrt{x} \sqrt{y}$

Now, we have:

$x-4=+-\sqrt{28}\\x-4=+-\sqrt{4*7}\\x-4=+-\sqrt{4}\sqrt{7}\\x-4=+-2\sqrt{7}$

Now we take 4 to the other side and isolate x:

$x-4=+-2\sqrt{7} \\x=4+-2\sqrt{7}$

first answer choice is right.