Question

How do you find the roots of `2x^2+ 7x -3 =x^2 +3x` using any method you choose?

Answer 1

We start by putting all terms to one side of the equation.

`2x^2 - x^2 + 7x - 3x - 3 = 0`

Next, combine like terms.

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

Since we are dealing with small numbers, we can easily discover whether or not this trinomial is factorable, and if it is, factor it. However, no two numbers add to `4` and multiply to `-3`. Hence, we will need to solve using what I find to be the next easiest method: the quadratic formula.

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

`x = (-4 +-sqrt(4^2 - 4 xx 1 xx -3))/(2 xx 1)`

`x = (-4 +-sqrt(28))/2`

`x = (-4 +- 2sqrt(7))/2`

`x = +-sqrt(7) - 2`

Hopefully this helps!