SOLUTION: use the quadratic formula to solve:3x^2+2x-4=0? A)x=-1 B)x=sqrt(13) C)x=-1-sqrt(13) D)x=-1/3 E)=-1+sqrt(13)/3

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: use the quadratic formula to solve:3x^2+2x-4=0? A)x=-1 B)x=sqrt(13) C)x=-1-sqrt(13) D)x=-1/3 E)=-1+sqrt(13)/3      Log On


   

Question 545446: use the quadratic formula to solve:3x^2+2x-4=0?
A)x=-1
B)x=sqrt(13)
C)x=-1-sqrt(13)
D)x=-1/3
E)=-1+sqrt(13)/3
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B2x-4=0 Start with the given equation.


Notice that the quadratic 3x%5E2%2B2x-4 is in the form of Ax%5E2%2BBx%2BC where A=3, B=2, and C=-4


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


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


x+=+%28-2+%2B-+sqrt%28+4--48+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-4%29 to get -48


x+=+%28-2+%2B-+sqrt%28+4%2B48+%29%29%2F%282%283%29%29 Rewrite sqrt%284--48%29 as sqrt%284%2B48%29


x+=+%28-2+%2B-+sqrt%28+52+%29%29%2F%282%283%29%29 Add 4 to 48 to get 52


x+=+%28-2+%2B-+sqrt%28+52+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-2+%2B-+2%2Asqrt%2813%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-2%2B2%2Asqrt%2813%29%29%2F%286%29 or x+=+%28-2-2%2Asqrt%2813%29%29%2F%286%29 Break up the expression.


x+=+%28-1%2Bsqrt%2813%29%29%2F%283%29 or x+=+%28-1-sqrt%2813%29%29%2F%283%29 Reduce


So the solutions are x+=+%28-1%2Bsqrt%2813%29%29%2F%283%29 or x+=+%28-1-sqrt%2813%29%29%2F%283%29