SOLUTION: i just need this factored 30000r(squared)-2225r-14=0. just need it factored i can take it from there.

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Question 242616: i just need this factored 30000r(squared)-2225r-14=0. just need it factored i can take it from there.
Found 2 solutions by Theo, jsmallt9:
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
standard form of quadratic equation is:

ax^2 + bx + c = 0

your equation is:

30000x^2 - 2225x - 14 = 0

I replaced r with x to standardize the formula. it can also be graphed with x but not with r.

a is the coefficient of the x^2 term.
b is the coeeficient of the x term.
c is a constant.

in your equation:

a = 30000
b = -2225
c = -14

discriminant of the quadratic formula in your equation is:

b^2 - 4ac = 4950625 - (-1680000) = 6630625 = 2575^2

this is a perfect square so your equation can be factored theoretically, but because the denominator of the quadratic formula is so large, the value of x will not be an integer, which means our factors will not be integers.

I used the quadratic formula which is the fall back position in cases where the factors cannot be found any other way.

Unless you have to find the factors manually, don't spend a lot of time trying to find them manually. If they can't be found easily, then use the quadratic formula.

the quadratic formula is:

x = ((-b) +/- (sqrt(b^2-4ac)))/(2a)

where:

a = 30000
b = -2225
c = -14

x = (-(-2225) +/- sqrt((2225)^2-4*30000*(-14)))/60000

x = -.0058333333

or:

x = .08

graph of your equation looks like this:

graph+%28600%2C600%2C-2%2C2%2C-1000%2C6000%2C3000x%5E2+-+2225x+-+14%29







Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
One could try to factor this directly. But with 30000 there are way too many possible factors for me to want to do this.

But we can use the Quadratic Formula to factor. We can find the solutions and then use the solutions to write the quadratic in factored form. With the help of a calculator this will, I think, be easier than trying the possible combinations of factors of 30000 and 14 until we find the one that works.

r+=+%28-%28-2225%29+%2B-+sqrt%28%28-2225%29%5E2+-+4%2830000%29%28-14%29%29%29%2F2%2830000%29
r+=+%28-%28-2225%29+%2B-+sqrt%284950625+-+4%2830000%29%28-14%29%29%29%2F2%2830000%29
r+=+%28-%28-2225%29+%2B-+sqrt%284950625+-+%28-1680000%29%29%29%2F2%2830000%29
r+=+%28-%28-2225%29+%2B-+sqrt%286630625%29%29%2F2%2830000%29
r+=+%28-%28-2225%29+%2B-+2575%29%2F2%2830000%29
r+=+%282225+%2B-+2575%29%2F60000
r+=+4800%2F60000 or r+=+%28-350%29%2F60000
r+=+48%2F600 or r+=+%28-35%29%2F6000
r+=+4%2F50 or r+=+%28-7%29%2F1200
r+=+2%2F25 or r+=+%28-7%29%2F1200

With these solutions, we can write the quadratic in factored form:
%2825r+-+2%29%281200r+%2B+7%29+=+0