SOLUTION: help me solve the equation. directions i was given: solve the following equation for x. {{{ 3x^2+4x-3=0 }}}

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: help me solve the equation. directions i was given: solve the following equation for x. {{{ 3x^2+4x-3=0 }}}      Log On


   

Question 174722: help me solve the equation.
directions i was given:
solve the following equation for x.
+3x%5E2%2B4x-3=0+
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B4x-3=0 Start with the given equation.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=4, and c=-3


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-%284%29+%2B-+sqrt%28+%284%29%5E2-4%283%29%28-3%29+%29%29%2F%282%283%29%29 Plug in a=3, b=4, and c=-3


x+=+%28-4+%2B-+sqrt%28+16-4%283%29%28-3%29+%29%29%2F%282%283%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--36+%29%29%2F%282%283%29%29 Multiply 4%283%29%28-3%29 to get -36


x+=+%28-4+%2B-+sqrt%28+16%2B36+%29%29%2F%282%283%29%29 Rewrite sqrt%2816--36%29 as sqrt%2816%2B36%29


x+=+%28-4+%2B-+sqrt%28+52+%29%29%2F%282%283%29%29 Add 16 to 36 to get 52


x+=+%28-4+%2B-+sqrt%28+52+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-4+%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+=+%28-4%2B2%2Asqrt%2813%29%29%2F%286%29 or x+=+%28-4-2%2Asqrt%2813%29%29%2F%286%29 Break up the expression.



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


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


which approximate to x=0.535 or x=-1.869