Sunday

September 25, 2016
Posted by **Anonymous** on Thursday, January 10, 2013 at 12:45am.

2x^2=5x+12

- Algebra 2 -
**Bosnian**, Thursday, January 10, 2013 at 2:59am2 x ^ 2 = 5 x + 12

Subtract 5 x + 12 to both sides

2 x ^ 2 - ( 5 x + 12 ) = 5 x + 12 - ( 5 x + 12 )

2 x ^ 2 - 5 x - 12 = 0 Divide both sides by leading coefficient ( 2 )

x ^ 2 - 5 x / 2 - 6 = 0 Add 6 to both sides

x ^ 2 - 5 x / 2 - 6 + 6 = 0 + 6

x ^ 2 - 5 x / 2 = 6

________________________________________

Take one half of the coefficient of x and square it.

In this case [ ( 5 / 2 ) / 2 ] ^ 2 = ( 5 / 4 ) ^ 2 = 25 / 16

________________________________________

Add 25 / 16 to both sides

x ^ 2 - 5 x / 2 + 25 / 16 = 6 + 25 / 16

________________________________________

Remark :

x ^ 2 - 5 x / 2 + 25 / 16 = ( x - 5 / 4 ) ^ 2

6 = 96 / 16

________________________________________

( x - 5 / 4 ) ^ 2 = 96 / 16 + 25 / 16

( x - 5 / 4 ) ^ 2 = 121 / 16

x - 5 / 4 = + OR - sqrt ( 121 / 16 )

x - 5 / 4 = + OR - 11 / 4 Add 5 / 4 to both sides

x - 5 / 4 + 5 / 4 = + OR - 11 / 4 + 5 / 4

x = + OR - 11 / 4 + 5 / 4

x1 = 11 / 4 + 5 / 4 = 16 / 4 = 4

x2 = - 11 / 4 + 5 / 4 = - 6 / 4 = - 3 / 2

For graph go on :

wolframalpha dot com

When page be open in rectangle type :

2 x ^ 2 = 5 x + 12

and click option =