Question

Solve the following quadratic equation by using the Quadratic Formula: 4x² + -3x + 9=2x+1 what are the values of x

Answer 1

`x = ( 5 )/(8) + (√( 103)i)/(8)`

or

`x = ( 5 )/(8) - (√( 103)i)/(8)`

Step-by-step explanation

The given equation is:

`4 {x}^(2) - 3x + 9 = 2x + 1`

We rewrite in the form ax² +bx+c=0 to get:

`4 {x}^(2) - 3x - 2x + 9 - 1= 0`

`4 {x}^(2) - 5x + 8= 0`

This implies that, a=4, b=-5,c=8.

The quadratic formula is given by,

`x = \frac{ - b \pm \sqrt{ {b}^(2) - 4ac} }{2a}`

We plug in the values to get,

`x = \frac{ - - 5\pm \sqrt{ {( - 5)}^(2) - 4(4)(8)} }{2(4)}`

`x = ( 5\pm √( - 103) )/(8)`

`x = ( 5\pm √( 103) i)/(8)`

`x = ( 5 )/(8) + (√( 103)i)/(8)`

Or

`x = ( 5 )/(8) - (√( 103)i)/(8)`