SOLUTION: solve for X by using quadratic formula. 3x2+x-2=0

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: solve for X by using quadratic formula. 3x2+x-2=0      Log On


   

Question 228192: solve for X by using quadratic formula.

3x2+x-2=0
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2Bx-2=0 Start with the given equation.


Notice that the quadratic 3x%5E2%2Bx-2 is in the form of Ax%5E2%2BBx%2BC where A=3, B=1, and C=-2


Let's use the quadratic formula to solve for "x":


x+=+%28-B+%2B-+sqrt%28+B%5E2-4AC+%29%29%2F%282A%29 Start with the quadratic formula


x+=+%28-%281%29+%2B-+sqrt%28+%281%29%5E2-4%283%29%28-2%29+%29%29%2F%282%283%29%29 Plug in A=3, B=1, and C=-2


x+=+%28-1+%2B-+sqrt%28+1-4%283%29%28-2%29+%29%29%2F%282%283%29%29 Square 1 to get 1.


x+=+%28-1+%2B-+sqrt%28+1--24+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-2%29 to get -24


x+=+%28-1+%2B-+sqrt%28+1%2B24+%29%29%2F%282%283%29%29 Rewrite sqrt%281--24%29 as sqrt%281%2B24%29


x+=+%28-1+%2B-+sqrt%28+25+%29%29%2F%282%283%29%29 Add 1 to 24 to get 25


x+=+%28-1+%2B-+sqrt%28+25+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-1+%2B-+5%29%2F%286%29 Take the square root of 25 to get 5.


x+=+%28-1+%2B+5%29%2F%286%29 or x+=+%28-1+-+5%29%2F%286%29 Break up the expression.


x+=+%284%29%2F%286%29 or x+=++%28-6%29%2F%286%29 Combine like terms.


x+=+2%2F3 or x+=+-1 Simplify.


So the solutions are x+=+2%2F3 or x+=+-1