SOLUTION: 3x squared + 12x = -2 I can find the square sign on my computer so I just wrote out 3x squared

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 3x squared + 12x = -2 I can find the square sign on my computer so I just wrote out 3x squared      Log On


   

Question 252256: 3x squared + 12x = -2
I can find the square sign on my computer so I just wrote out 3x squared
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

3x%5E2%2B12x=-2 Start with the given equation.


3x%5E2%2B12x%2B2=0 Add 2 to both sides.


Notice that the quadratic 3x%5E2%2B12x%2B2 is in the form of Ax%5E2%2BBx%2BC where A=3, B=12, 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-%2812%29+%2B-+sqrt%28+%2812%29%5E2-4%283%29%282%29+%29%29%2F%282%283%29%29 Plug in A=3, B=12, and C=2


x+=+%28-12+%2B-+sqrt%28+144-4%283%29%282%29+%29%29%2F%282%283%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144-24+%29%29%2F%282%283%29%29 Multiply 4%283%29%282%29 to get 24


x+=+%28-12+%2B-+sqrt%28+120+%29%29%2F%282%283%29%29 Subtract 24 from 144 to get 120


x+=+%28-12+%2B-+sqrt%28+120+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-12+%2B-+2%2Asqrt%2830%29%29%2F%286%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-12%2B2%2Asqrt%2830%29%29%2F%286%29 or x+=+%28-12-2%2Asqrt%2830%29%29%2F%286%29 Break up the expression.


x+=+%28-6%2Bsqrt%2830%29%29%2F%283%29 or x+=+%28-6-sqrt%2830%29%29%2F%283%29 Reduce.


So the solutions are x+=+%28-6%2Bsqrt%2830%29%29%2F%283%29 or x+=+%28-6-sqrt%2830%29%29%2F%283%29


which approximate to x=-0.174 or x=-3.826