SOLUTION: Solve the equation: 3x^2 + 15x + 18 = 0

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Question 96252: Solve the equation:
3x^2 + 15x + 18 = 0
Found 2 solutions by jim_thompson5910, prabhjyot:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's use the quadratic formula to solve for x:


Starting with the general quadratic

ax%5E2%2Bbx%2Bc=0

the general solution using the quadratic equation is:

x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29

So lets solve 3%2Ax%5E2%2B15%2Ax%2B18=0 ( notice a=3, b=15, and c=18)

x+=+%28-15+%2B-+sqrt%28+%2815%29%5E2-4%2A3%2A18+%29%29%2F%282%2A3%29 Plug in a=3, b=15, and c=18



x+=+%28-15+%2B-+sqrt%28+225-4%2A3%2A18+%29%29%2F%282%2A3%29 Square 15 to get 225



x+=+%28-15+%2B-+sqrt%28+225%2B-216+%29%29%2F%282%2A3%29 Multiply -4%2A18%2A3 to get -216



x+=+%28-15+%2B-+sqrt%28+9+%29%29%2F%282%2A3%29 Combine like terms in the radicand (everything under the square root)



x+=+%28-15+%2B-+3%29%2F%282%2A3%29 Simplify the square root (note: If you need help with simplifying the square root, check out this solver)



x+=+%28-15+%2B-+3%29%2F6 Multiply 2 and 3 to get 6

So now the expression breaks down into two parts

x+=+%28-15+%2B+3%29%2F6 or x+=+%28-15+-+3%29%2F6

Lets look at the first part:

x=%28-15+%2B+3%29%2F6

x=-12%2F6 Add the terms in the numerator
x=-2 Divide

So one answer is
x=-2



Now lets look at the second part:

x=%28-15+-+3%29%2F6

x=-18%2F6 Subtract the terms in the numerator
x=-3 Divide

So another answer is
x=-3

So our solutions are:
x=-2 or x=-3

Notice when we graph 3%2Ax%5E2%2B15%2Ax%2B18, we get:

+graph%28+500%2C+500%2C+-13%2C+8%2C+-13%2C+8%2C3%2Ax%5E2%2B15%2Ax%2B18%29+

and we can see that the roots are x=-2 and x=-3. This verifies our answer

Answer by prabhjyot(165) About Me  (Show Source):
You can put this solution on YOUR website!
3x%5E2+%2B+15x+%2B+18+=+0
Compare the above equation with standard quadratic equationax%5E2%2Bbx%2Bc=0
we get
a = 3
b = 15
c = 18

Discriminant: b%5E2-4ac+=+15+2-4%2A3%2A18+=+9+
Discriminant (9) is greater than zero. The equation has two solutions.
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
x+=+%28-15+%2B-+sqrt%28+15%5E2-4%2A3%2A18+%29%29%2F%282%2A3%29+
or
x+=%28-15+%2B-+3%29+%2F+2%2A3
or
x1+=+-12+%2F+6+=+-2
x2+=+-18+%2F+6+=+-3
Equation factored:
3%28x%2B2%29%28x%2B3%29