Question

How do you solve `2y² + 2y = 1` using the quadratic formula?

Answer 1

`y=-1/2+-sqrt(3)/2`
(see below for use of quadratic formula)

Explanation:

`2y^2+2y=1` is equivalent to `color(red)(2)y^2+color(blue)(2)ycolor(green)(-1)`

Using the general quadratic:
`color(white)("XXX")color(red)(a)y^2+color(blue)(b)y+color(green)(c)=0`
and applying the general quadratic formula
`color(white)("XXX")y=(-color(blue)(b)+-sqrt(color(blue)(b)^2-4(color(red)(a))(color(green)(c))))/(2(color(red)(a))`

We have
`color(white)("XXX")y=(-color(blue)(2)+-sqrt(color(blue)(2)^2-4(color(red)(2))(color(green)(-1))))/(2(color(red)(2))`

`color(white)("XXX")y=(-2+-sqrt(12))/4=-1/2+-sqrt(3)/2`