let number be ....

if a number () is added to its square (),the result is  

 or 

.....use quadratic formula 

Solved by pluggable solver: Quadratic Formula

Let's use the quadratic formula to solve for x:

Starting with the general quadratic

the general solution using the quadratic equation is:

So lets solve  ( notice , , and )

 Plug in a=1, b=1, and c=-42

 Square 1 to get 1 

 Multiply  to get 

 Combine like terms in the radicand (everything under the square root)

 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)

 Multiply 2 and 1 to get 2

So now the expression breaks down into two parts

 or 

Lets look at the first part:

 Add the terms in the numerator

 Divide

So one answer is

Now lets look at the second part:

 Subtract the terms in the numerator

 Divide

So another answer is

So our solutions are:

 or 

so, one answer is  and another answer is  

check: