# The sum of a number and its square is 5 times the number. What is the number?

### 4 Answers | Add Yours

The sum of a number and its square is 5 times the number. Let the number be X.

X + X^2 = 5*X

=> X^2 = 5X - X

=> X^2 = 4X

=> X^2 - 4X = 0

=> X(X - 4) = 0

=> X = 0 and X = 4

**For the numbers 0 and 4, the sum of the number and its square is 5 times the number.**

QUESTION:-

The sum of a number and its square is 5 times the number. Let the number be X.

SOLUTION:-

We can solve this problem by factorization.

Let x be the unknown number;

`x+x^2=5x`

`x^2+x-5x=0`

`x^2-4x=0`

`x(x-4)=o`

`x=0`

`x=4`

Hence Solved!!

The answers for this problem are as follows:-

- x = 0
- x = 4.

This problem can also be solved by quadratic equation formula also.

` `

The sum refers to addition, so you know you must add the number (represented by the variable x) and the number (x) squared.

x+x^2

This equation is equal to 5 times the number or 5*x

x+x^2=5x

To get x by itself, you must first subtract x from both sides

x^2=5x-x or *x^2=4x*

The easiest way to continue is to make everything equal to zero (put everything on the same side)

x^2-4x=0

Factor out the x they have in common

x(x-4)

Set your factors equal to zero

**x=0 ** x-4=0

**x=4**

The sum of a number and its square is 5 times the number. What is the number?