# The sum of an integer and its square is 90. Find the number

2
by Nicoleyyy

2015-09-30T19:12:37+08:00

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The integer is 9.
9 + 9^2 (or 81) = 90.
• Brainly User
2015-10-01T11:55:57+08:00

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
Equation: Let the integer be x.

x² + x = 90

Equate to zero to solve the quadratic equation:
x² + x - 90 = 0

Factor:
(x + 10) (x - 9) = 0

Solve for roots (x):
x + 10 = -10                      x - 9 = 0
x = -10                              x = 9

Choose the positive root, x = 9, the integer.

To check:
(9)² + 9 = 90
81 + 9 = 90
90 = 90