SOLUTION: 10x^-2+33x^-1-7=0 How do you solve this equation?

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Question 652630: 10x^-2+33x^-1-7=0
How do you solve this equation?
Found 2 solutions by MathLover1, stanbon:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
10%28x%5E%28-2%29%29%2B33x%5E%28-1%29-7=0+

%2810%2Fx%5E2%29%2B%2833%2Fx%29-7=0+....find common denominator

%2810x%2B33x%5E2-7x%5E3%29%2Fx%5E3=0+

10x%2B33x%5E2-7x%5E3=0%2Ax%5E3+

-7x%5E3%2B33x%5E2%2B10x=0+...factor

x%28-7x%5E2%2B33x%2B10%29=0+... replace 33x with 35x-2x

x%28-7x%5E2%2B35x-2x%2B10%29=0+...group

x%28%28-7x%5E2%2B35x%29-%282x-10%29%29=0+

x%28-7x%28x-5%29-2%28x-5%29%29=0+

x%28-7x-2%29%28x-5%29%29=0+

x%2A-1%287x%2B2%29%28x-5%29%29=0+

-x%287x%2B2%29%28x-5%29%29=0+

solutions:

if -x=0+ ....->...x=0

if 7x%2B2=0+....->...7x=-2+..->...x=-2%2F7+

if x-5=0+...->...x=5


+graph%28+600%2C+600%2C+-5%2C+7%2C+-5%2C+30%2C+-x%2A%287x%2B2%29%2A%28x-5%29%29+






Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
10x^-2+33x^-1-7=0
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It's a quadratic with variable x^-1
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Let w = x^-1.
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10w^2 + 33w -7 = 0
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10w^2 + 35w-2w - 7 = 0
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5w(2w+7)-(2w+7) = 0
(2w+7)(5w-1) = 0
w = -7/2 or w = 1/5
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Solve for x:
x^-1 -7/2 or x^-1 = 1/5
---
x = -2/7 or x = 5
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Cheers,
Stan H.
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