If an integer is added to its square, the sum is 90. Find the integer

1.	If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.
Answer» Assume the integer be x. Then its square will be x². And given, their sum is 90 ⇒ x + x² = 90 ⇒ x² + x – 90 = 0 Solving for x by factorization method, we have x² + 10x – 9x – 90 = 0 ⇒ x(x + 10) – 9(x + 10) = 0 ⇒ (x + 10)(x – 9) = 0 Now, either x + 10 = 0 ⇒ x = –10 Or, x – 9 = 0 ⇒ x = 9 Thus, the values of the integer are 9 and -10 respectively.

If an integer is added to its square, the sum is 90. Find the integer with the help of quadratic equation.

Answer»

Assume the integer be x. Then its square will be x².

And given, their sum is 90

⇒ x + x² = 90

⇒ x² + x – 90 = 0

Solving for x by factorization method, we have

x² + 10x – 9x – 90 = 0

⇒ x(x + 10) – 9(x + 10) = 0

⇒ (x + 10)(x – 9) = 0

Now, either x + 10 = 0 ⇒ x = –10

Or, x – 9 = 0 ⇒ x = 9

Thus, the values of the integer are 9 and -10 respectively.