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

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justaguide | College Teacher | (Level 2) Distinguished Educator

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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.

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sid-sarfraz | Student, Graduate | (Level 2) Salutatorian

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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. 

` `

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rachellopez | Student, Grade 12 | (Level 1) Valedictorian

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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

atyourservice's profile pic

atyourservice | Student, Grade 11 | (Level 3) Valedictorian

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

x + x^2 = 5x
 
subtract x
 
x^2 = 5x - x
 
x^2 = 4x
 
now move them to the same side
 
x^2 - 4x =0
 
factor out the gcf
 
x(x-4) = 0
 
set x and x-4 equal to 0
 
x=0
 
x-4=0
 
x= 4
 
x= 0 x= 4
 

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