If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integ

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If 7 times the square of an integer is added to 5 times the integer, the result is 2. Find the integer.

• Let the integer be "x".
• Square the integer: x^2
• 7 times the square: 7x^2
• 5 times the integer: 5x
• Add them together: 7x^2 + 5x
• The result is means an equation, so we set 7x^2 + 5x equal to 2

7x^2 + 5x = 2

This is a quadratic equation. To get it into standard form, we subtract 2 from each side:
7x^2 + 5x - 2 = 2 - 2
7x^2 + 5x - 2 = 0

Type this problem into our search engine, and we get two solutions:

1. x = 2/7
2. x= -1

The problem asks for an integer, so our answer is x = -1.

Let's check our work by plugging x = -1 into the quadratic:
7x^2 + 5x - 2 = 0
7(-1)^2 + 5(-1) - 2 ? 0
7(1) - 5 - 2 ? 0
0 = 0

So we verified our answer, x = -1.