how do i find the correct answer?

Question

If a number is added to three times its square, the result is 14. Find all such numbers.

1) 2 and -2

2) 2

3)2 and - 

4) -2

what is the correct answer?

Answer 1

Hi Maya.

Call the unknown number x

Three times its square is

3*x² or 3x²

The sum of x and three times its square is 14.

x + 3x² = 14

-14 -14 (move everything to left side)

--------------------

x + 3x² -14 = 0

Reorganize in descending powers of x

3x² + x - 14 = 0

There is a trick to factoring trinomials with a

number in front of the x² term.

Multiply 3 * -14 = -42

Find factors of -42 that add up to the

coefficient in front of x. It is 1 in this case.

The factors of -42 that add to 1 are

7 and -6. Rewrite x as 7x - 6x

3x² + x - 14 = 0

3x² + 7x - 6x - 14 = 0

Next, group

(3x² + 7x) + (-6x - 14) = 0

Factor

x(3x + 7) + -2(3x+7) = 0

Factor out the (3x+7)

(3 x +7)(x + -2) =0

(3x + 7)(x - 2) = 0

So, 3x+7 =0 or x - 2 = 0

Can you solve each of these for x?

Answer 2

Translate the English into math:

x+3x²=14,

This factors nicely to give you the answer.