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## Homework Statement

Lets say you have Ax + Bx^2 + C = 0

Usually I would use the Quadratic formula in this situation.

But what if you do this

x( A + Bx ) + C = 0

x( A + Bx ) = -C

Couldn't you then say

**x = -C**

and

A + Bx = -C

**x = (-C - A) / B**

?

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- Thread starter yougene
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- #1

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Lets say you have Ax + Bx^2 + C = 0

Usually I would use the Quadratic formula in this situation.

But what if you do this

x( A + Bx ) + C = 0

x( A + Bx ) = -C

Couldn't you then say

and

A + Bx = -C

?

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- #2

Homework Helper

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yougene said:## Homework Statement

Lets say you have Ax + Bx^2 + C = 0

Usually I would use the Quadratic formula in this situation.

But what if you do this

x( A + Bx ) + C = 0

x( A + Bx ) = -C

Couldn't you then say

x = -C

and

A + Bx = -C

x = (-C - A) / B

?

Well you could say that, but it won't be correct. If you sub x=-C you will get

-C(A-BC) = -AC+BC

and that is not the right side of the equation in red.

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- #4

Mentor

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- #5

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So then my equation would work only if C = 0.

@Mark44

So if my C = -1 then saying

Ax^2 + Bx = 1

would be a valid way to solve the equation?

Or are you saying

Ax^2 + Bx + C = 1

would be valid to solve for?

- #6

Gold Member

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yougene said:Couldn't you then say

x = -C

and

A + Bx = -C

No. Why do you think that? All that is telling you is that x and (A+Bx) are always -C when multiplied together if x is a solution to the quadratic formula. That doesn't tell you anything about what x actually is. Remember, the quadratic formula has 2 solutions so you have to get 2 numbers out of it for x.

- #7

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yougene said:So then my equation would work only if C = 0.

I believe that would be correct. If you had

x (A+Bx) = 0

then either (x) or (A+Bx) must be zero, or both. The two solutions would be

x =0 and

x=-A/B

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