2 Answers

ChickenSoups · Answer 1 · 2020-08-19T14:13:33+0000

Hello!

The answer is:

The correct answer is the first option.

(x-4)^(2)=4+-2√(7)

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!

Sertorio Noronha · Answer 2 · 2020-08-24T15:45:06+0000

Answer:

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.