Question

How do you solve `2x^2-x= -5` using the quadratic formula?

Answer 1

The solutions for the equation are:

`color(green)( x = (1+sqrt(-39))/4, color(green)( x = (1-sqrt(-39))/4`

Explanation:

`2x^2 - x = -5`

`2x^2 - x + 5 = 0`

The equation is of the form `color(blue)(ax^2+bx+c=0` where:
`a=2, b=-1, c=5`

The Discriminant is given by:

`Delta=b^2-4*a*c`

`= (-1)^2-(4* 2 * 5)`

`= 1 - 40 = - 39`

The solutions are found using the formula
`x=(-b+-sqrtDelta)/(2*a)`

`x = (-(-1)+-sqrt(-39))/(2*2) = (1+-sqrt(-39))/4`

The solutions are:

• `color(green)( x = (1+sqrt(-39))/4`

• `color(green)( x = (1-sqrt(-39))/4`