SOLUTION: In using the factoring method of solving quadratic equations, we put it in the form:
(x+a)(x+b) = 0. Where a and b are two constants (think of them as two “numbers”).
If the
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Question 326332: In using the factoring method of solving quadratic equations, we put it in the form:
(x+a)(x+b) = 0. Where a and b are two constants (think of them as two “numbers”).
If the right-hand side of this equation is not zero (let’s say another constant "c"), do you think it can be solved? If so, how? If not, why not?
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let's presume you are faced with the equation:
(x\ -\ \beta)\ =\ \gamma)
Where 
, 
, and 
are constants.
Step one is to apply FOIL to the two binomials in the LHS.
x\ +\ \alpha\beta\ =\ \gamma)
Then add 
to both sides.
x\ +\ \alpha\beta\ -\ \gamma\ =\ 0)
Then combine the constants so that )
and 
to write:
Then, if you can find numbers 
and 
such that 
and 
, then you can factor your equation:
(x\ +\ q)\ =\ 0)
which has roots 
and 
barring that you can use the quadratic formula to write:
c}}{2(1)})
to find your two roots.
John
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