a whole number increased by its square is twenty more than twice itself. a.) Write an equation that represents the statement.

Question

a.) Write an equation that represents the statement.

 

B.) Solve the equation and find the number.

Answer 1

A whole number increased by its square is twenty more than twice itself.

Call the number x just for convenience

Note that "increased by" would be addition and "is" means equals

 

a)    x + x² = 2x + 20

 

That is the initial version of the equation as given in the problem

Let's arrange that into a basic quadratic equation of the form ax² + bx + c = 0

 

      x² + x - 2x - 20 = 0

      x² - x - 20 = 0

 

b)   We can factor this equation easily rather than using the quadratic

       Looking at the coefficients and constant we need the factors of the constant -20 that add to the

       x coefficient of -1 so for our factor use -5,4 since (-5)(4) = -20 and -5 + 4 = -1

     

       x² - x - 20 = (x-5)(x+4)

      Setting that equal to zero we have

 

      (x-5)(x+4) = 0

 

      For this to be true either x-5 = 0    or     x + 4 = 0

       So x = 5 or x = -4

 

Check:  5² - 5 - 20 = 0        (-4)² - (-4) -20 = 0

            25 - 25 = 0             16 + 4 - 20 = 0

            0 = 0                      20 - 20 = 0

                                          0 = 0

 

We can see that both our answers are correct