Question

Find a negative real number such that the square of the sum of the number and

25 is equal to 36

Answer 1

"The square of the sum of the number and 25 is equal to 36" translates to

`(n+25)^2=36`

Take square root of both sides:


`|n+25|=6\quad\Longrightarrow\quad n+25 = 6\ \text{ or }\ n+25=-6`

Then subtract both sides by 25:


`n = 6-25\ \text{ or }\ n=-6-25\\\ \\\boxed{n=-19\ \text{or}\ n=-31}`

Hope this helps.