The sum of 3 times the square of the number and 6 times the number is equal to twice the square of that number, decreased by 8. Find the number.

Answer 1

Let's use the variable x to represent the unknown number.

Then " the sum of 3 times the square of a number and 6 times the number " would be represented by:

3x ² + 6x

The text "twice the square of that number decreased by 8" would be represented by: 2x ² - 8

These two expression would be equal to one another:

3x ² + 6x = 2x ² - 8

Now solve this equation using inverse operations and factoring:

3x ² + 6x = 2x ² - 8

3x ² + 6x - 2x ² = 2x ² - 8 - 2x ²

x² + 6x = -8

x² + 6x + 8 = -8 + 8

x² + 6x + 8 = 0

Now factoring this polynomial to:

(x + 4) (x + 2) = 0

x = -4 and x = -2

The solutions to this problem are -4 and -2

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