How do I answer this question? `(n-5)^2=32`

Expert Answers

An illustration of the letter 'A' in a speech bubbles

`(n-5)^2 = 32`

`(n-5) = +-sqrt32`

     `n = 5+-sqrt32`

    `n = 5+-sqrt(16xx2)`

     `n =5+-sqrt16xxsqrt2`

     `n = 5+-4sqrt2`

 

So the answers are;

`n = 5+4sqrt2`

`n = 5-4sqrt2`

Approved by eNotes Editorial Team
An illustration of the letter 'A' in a speech bubbles

`(n-5)^2=32`

To solve, expand left side.

`(n-5)(n-5)=32`

`n^2-10n+25=32`

Then, set one side equal to zero.

`n^2-10n+25-32=32-32`

`n^2-10n-7=0`

And, use the quadratic formula to solve for n.

 

`n=(-b+-sqrt(b^2-4ac))/(2a)=(-(-10)+-sqrt((-10)^2-4*1*(-7)))/(2*1) `

`n=(10+-sqrt(100+28))/2=(10+-sqrt128)/2=(10+-8sqrt2)/2=5+-4sqrt2`

Hence, `n=5+4sqrt2`   and   `n=5-4sqrt2` .

Approved by eNotes Editorial Team