Find a Number by the Sum of the Number and Its Square Calculator

Welcome to the free online calculator to find the number by a given sum of the number and its square. For example, the sum of a number and its square is 72. What is this number?

Let this number be x.

According to the above question, we can get an equation

x + x² = 72

Simplify the equation.

x + x² = 72

x² + x – 72 = 0

Now, we get a quadratic equation, the next key is to solve this quadratic equation. The answer to the quadratic equation can be calculated using the formula method or the factorization method.

The quadratic formula is

Among them, a = 1, b = 1, c = -72. So, we can get the value of x

b² – 4ac = 1² – 4 * 1 * (-72) = 1 + 288 = 289

x = -1 + √2892*1 = -1 + 172 = 162 = 8

Or

x = -1 – √2892*1 = -1 – 172 = -182 = -9

Or use the factorization method directly.

x² + x – 72 = 0

(x – 8) (x + 9) = 0

x = 8 or x = -9

So, this number is 8 or -9.

Verify.

8 + 8² = 8 + 64 = 72

Or

-9 + (-9)² = 81 – 9 = 72

Correct.

The whole process is not difficult, the key is the solution of the quadratic equation. If you don’t want to calculate, it is recommended to use the free calculator available on this page to find a number by the sum of the number and its square. Omits all steps and displays the answer in milliseconds.

Next, we will introduce how to use the calculator.

Using the calculator is simple, with only two steps:

Next, let’s look at some examples.