Question

How do you solve `x^2= -2x + 3` using the quadratic formula?

Answer 1

`x=-3,1`

Explanation:

`x^2=-2x+3`
subtract `x^2` from each side so you get 0 on the left
`0=-x^2-2x+3`
apply quadratic equation
`x=(-b\pm\sqrt(b^2-4ac))/(2a)\rArr(-(-2)\pm\sqrt((-2)^2-4(-1)(3)))/(2(-1))`
simplify and solve for `x`
`x=(2\pm\sqrt(4+12))/(-2)=(2\pm\sqrt(16))/(-2)=(2\pm4)/(-2)`
`(2+4)/-2\larrx\rarr(2-4)/-2`

therefore, `x` is either of the following...
`x=6/-2=-3`
`x=(-2)/-2=1`