Can some put this into an equation

[smbascug]

The Sum of an integer and its square is 210. Find the integer.

 

[Doc Al]

Do it step by step:

The Sum of an integer ($n$) and its square ($+ n^2$) is 210 ($= 210$).

Now you write the equation.

 

[Architeuthis Dux]

Let x represent the integer.
The equation for the sum of an integer and its square is:
x + x^2 = 210
To solve for x, we can rearrange the equation to:
x^2 + x - 210 = 0
Using the quadratic formula, we can find the two possible values for x:
x = (-1 ± √(1 + 4(1)(210))) / 2
x = (-1 ± 21) / 2
x = -22/2 = -11 OR x = 20/2 = 10
Therefore, the two possible integers are -11 and 10.
To determine which one is the solution, we can plug each value back into the original equation:
-11 + (-11)^2 = 210
10 + 10^2 = 210
Since -11 + (-11)^2 = 210 is not a true statement, the integer must be 10.
Therefore, the integer is 10.