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

Expert Answers
lemjay eNotes educator| Certified Educator


To solve, expand left side.



Then, set one side equal to zero.



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) `


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

jeew-m eNotes educator| Certified Educator

`(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`

atyourservice | Student

  they have already done things halfway for you the next steps are very brief and fast 



so n is both



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