Question

PLEASE HELP ME NOW!!

Answer 1

Hello!

The answer is:

The correct answer is the first option.

`(x-4)^(2)=4+-2√(7)`

Why?

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

`√(ab)=√(a)√(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) }=√(28)\\(x-4)=√(4*7)\\\\x=4+-(√(4)*√(7))\\\\x=4+-2√(7)`

Hence, the correct answer is the first option.

`(x-4)^(2)=4+-2√(7)`

Have a nice day!

Answer 2

`x=4+-2√(7)`

Explanation:

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

`(x-4)^2=28\\√((x-4)^2) =+-√(28) \\x-4=+-√(28)`

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

Property:
`√(x*y)=√(x) √(y)`

Now, we have:

`x-4=+-√(28)\\x-4=+-√(4*7)\\x-4=+-√(4)√(7)\\x-4=+-2√(7)`

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

`x-4=+-2√(7) \\x=4+-2√(7)`

first answer choice is right.