Question

If a number is added to twice its square, the result is 6. How do you find the number?

1. List item

Answer 1

The number could be `1 1/2` or `-2`.

Explanation:

From the data, taking the number to be `x`, we write:

`2x^2+x=6`

Subtract `6` from both sides.

`2x^2+x-6=0`

Factorise.

`2x^2+4x-3x-6=0`

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

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

`2x-3=0` or `x+2=0`

`x=3/2=1 1/2` or `x=-2`

Answer 2

I get two numbers: `x=-2, 6/4=3/2`

Explanation:

Let's have the unknown number be `x`.

If a number:

`x`

is added to twice it's square:

`x+2x^2`

the result is 6:

`x+2x^2=6`

Now let's find the number:

`2x^2+x-6=0`

using the quadratic formula:

`x=(-b+-sqrt(b^2-4ac))/(2a)`

`x=(-1+-sqrt(1^2-4(2)(-6)))/(2(2))`

`x=(-1+-sqrt(1^2+48))/(4)`

`x=(-1+-sqrt(49))/(4)`

`x=(-1+-7)/(4)`

`x=-2, 6/4=3/2`