The sum of a number and its square is 110. Find the numbers.

Question

PLZ i really need help. Algebra

Answer 1

Let x be the number you are trying to find.

Then its square is x*x or x^2.

 

Now, X^2 + x = 110 or x^2 + x - 110 = 0 

 

This can be factored into (x + 11) (x -10) = 0

 

That means x = 10 or x = -11

 

The sum of 10 and its square, which is 100, is 110

 

the sum of -11 and its square, which is 121, is also 110.

 

This problem has two answers negative 11 and positive 10.

Answer 2

Number: X             Number squared = X^2            Sum= X+ (X^2)

 

so   X+ (X^2) = 110   as given

 

So (X^2) + X -110 = 0

 

(x+11) (x-10) = 0

 

so x=-11, 10

 

quick check:  (-11)^2 + (-11) = 121-11 = 110

                    (10)^2 + 10 = 100+10 = 110

 

so both answers are valid (which are 10 and -11). Note that you coul also use quadratic equation to come up with the answers.