SOLUTION: {{{3x^2=-12x-1}}} solve using the quadratic formula. I can do the first few steps. I am completely lost on the math involved between the last two steps.

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: {{{3x^2=-12x-1}}} solve using the quadratic formula. I can do the first few steps. I am completely lost on the math involved between the last two steps.      Log On


   

Question 169644: 3x%5E2=-12x-1 solve using the quadratic formula. I can do the first few steps. I am completely lost on the math involved between the last two steps.
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2=-12x-1 Start with the given equation


3x%5E2%2B12x%2B1=0 Add 12x to both sides. Add 1 to both sides.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=3, b=12, and c=1


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%281%29+%29%29%2F%282%283%29%29 Plug in a=3, b=12, and c=1


x+=+%28-12+%2B-+sqrt%28+144-4%283%29%281%29+%29%29%2F%282%283%29%29 Square 12 to get 144.


x+=+%28-12+%2B-+sqrt%28+144-12+%29%29%2F%282%283%29%29 Multiply 4%283%29%281%29 to get 12


x+=+%28-12+%2B-+sqrt%28+132+%29%29%2F%282%283%29%29 Subtract 12 from 144 to get 132


x+=+%28-12+%2B-+sqrt%28+132+%29%29%2F%286%29 Multiply 2 and 3 to get 6.


x+=+%28-12+%2B-+2%2Asqrt%2833%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%2833%29%29%2F%286%29 or x+=+%28-12-2%2Asqrt%2833%29%29%2F%286%29 Break up the expression.


So the answers are x+=+%28-12%2B2%2Asqrt%2833%29%29%2F%286%29 or x+=+%28-12-2%2Asqrt%2833%29%29%2F%286%29


which approximate to x=-0.085 or x=-3.915

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
solve using the quadratic formula. I can do the first few steps. I am completely lost on the math involved between the last two steps.
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3x%5E2=-12x-1
3x%5E2%2B12x%2B1+=+0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 3x%5E2%2B12x%2B1+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A3%2A1=132.

Discriminant d=132 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+132+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+132+%29%29%2F2%5C3+=+-0.0851457844873238
x%5B2%5D+=+%28-%2812%29-sqrt%28+132+%29%29%2F2%5C3+=+-3.91485421551268

Quadratic expression 3x%5E2%2B12x%2B1 can be factored:
3x%5E2%2B12x%2B1+=+%28x--0.0851457844873238%29%2A%28x--3.91485421551268%29
Again, the answer is: -0.0851457844873238, -3.91485421551268. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+3%2Ax%5E2%2B12%2Ax%2B1+%29

Ignore what the solver says about the factors, it's not right unless the coefficient of the x^2 term is 1.
The solutions are:
-2 + sqrt(33)/3
-2 - sqrt(33)/3