Question

How do you solve `2x^2 + 2x – 1 = 0`?

Answer 1

`x = (-1 +- sqrt3)/2`

Explanation:

To solve this, we will use the quadratic formula. We know that this is in standard quadratic form, or `ax^2 + bx + c`, where `a = 2`, `b = 2`, and `c = -1`.

The quadratic formula is:
`x = (-b +- sqrt(b^2 - 4ac))/(2a)`

Now plug in the values of `a`, `b`, and `c` into the formula to find the value of `x`:
`x = (-2 +- sqrt(2^2 - 4(2)(-1)))/(2(2))`

`x = (-2 +- sqrt(4 + 8))/4`

`x = (-2 +- sqrt12)/4`

`x = (-2 +- 2sqrt3)/4`

`x = (-1 +- sqrt3)/2`

Hope this helps!