SOLUTION: 5x to the 2 power +9x+1=0

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Question 102616: 5x to the 2 power +9x+1=0
Found 2 solutions by jim_thompson5910, edjones:
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 5%2Ax%5E2%2B9%2Ax%2B1=0 ( notice a=5, b=9, and c=1)




x+=+%28-9+%2B-+sqrt%28+%289%29%5E2-4%2A5%2A1+%29%29%2F%282%2A5%29 Plug in a=5, b=9, and c=1



x+=+%28-9+%2B-+sqrt%28+81-4%2A5%2A1+%29%29%2F%282%2A5%29 Square 9 to get 81



x+=+%28-9+%2B-+sqrt%28+81%2B-20+%29%29%2F%282%2A5%29 Multiply -4%2A1%2A5 to get -20



x+=+%28-9+%2B-+sqrt%28+61+%29%29%2F%282%2A5%29 Combine like terms in the radicand (everything under the square root)




x+=+%28-9+%2B-+sqrt%2861%29%29%2F10 Multiply 2 and 5 to get 10

So now the expression breaks down into two parts

x+=+%28-9+%2B+sqrt%2861%29%29%2F10 or x+=+%28-9+-+sqrt%2861%29%29%2F10


Now break up the fraction


x=-9%2F10%2Bsqrt%2861%29%2F10 or x=-9%2F10-sqrt%2861%29%2F10




So these expressions approximate to

x=-0.118975032409335 or x=-1.68102496759067


So our solutions are:
x=-0.118975032409335 or x=-1.68102496759067

Notice when we graph 5%2Ax%5E2%2B9%2Ax%2B1, we get:



when we use the root finder feature on a calculator, we find that x=-0.118975032409335 and x=-1.68102496759067.So this verifies our answer

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 5x%5E2%2B9x%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=%289%29%5E2-4%2A5%2A1=61.

Discriminant d=61 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-9%2B-sqrt%28+61+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%289%29%2Bsqrt%28+61+%29%29%2F2%5C5+=+-0.118975032409335
x%5B2%5D+=+%28-%289%29-sqrt%28+61+%29%29%2F2%5C5+=+-1.68102496759067

Quadratic expression 5x%5E2%2B9x%2B1 can be factored:
5x%5E2%2B9x%2B1+=+%28x--0.118975032409335%29%2A%28x--1.68102496759067%29
Again, the answer is: -0.118975032409335, -1.68102496759067. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+5%2Ax%5E2%2B9%2Ax%2B1+%29