SOLUTION: Solve for x x(x+2)(x-2)=35805 Thankyou ^^ Btw, x=33 but how and why?

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Question 567822: Solve for x
x(x+2)(x-2)=35805
Thankyou ^^

Btw, x=33
but how and why?

Found 2 solutions by richard1234, Alan3354:
Answer by richard1234(7193) (Show Source):
You can put this solution on YOUR website!
35805 = 31*33*35, x = 33

However it's a cubic equation so by the fundamental theorem of algebra, there should be three roots. Upon simplifying the LHS we have

We know x-33 is a factor so we can factor the LHS as (x-33)P(x) where P(x) is another polynomial. To find P(x) we divide the LHS by x-33 to obtain

By the quadratic formula, this has roots in the complex plane.

Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
Solve for x
x(x+2)(x-2)=35805

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There's a method to solve cubics, but it's complex and tedious.
If I didn't know 33 was a root, I would graph it.
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With a large coefficient, the 35805, and only -4 times the x term, there's likely to be a root near the cube root of 35805.
, close to 33, so checking for 33 being a root is reasonable.
The other 2 roots are complex.