SOLUTION: Algebraically find the EXACT ROOTS in simplest form for: x/-7=(x+1)/(x-11)

Question 177920: Algebraically find the EXACT ROOTS in simplest form for: x/-7=(x+1)/(x-11)
Answer by gonzo(654) (Show Source): You can put this solution on YOUR website!
this equation doesn't have any roots.
when you solve for the roots you get a complex number.
complex number means there are no roots.
here's how i did it.
your equation is:

muiltiply both sides by -7 to get:

multiply both sides by (x-11) to get:

simplify to get:

add 7x to both sides to get:

add 7 to both sides to get":

simplify to get:

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you can solve this using the quadratic formula or completing the squares.
either way will get you the same answer.
i'll use the quadratic formula first:
a = 1 = coefficient of the x^2 term.
b = -4 = coefficient of the x term.
c = 7 = constant term.
quadratic formula is:

substituting values for a,b,c gets:

this becomes:

which becomes:

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you can also solve this by completing the squares as follows:
your equation after manipulating it is:

this is the same place where we solved it using the quadratic formula.
this time, however, we will complete the squares.
subtract 7 from both sides to get:

your equation becomes:

you add 4 to both sides to get:

you take the square root of both sides to get:
= +/-
you add 2 to both sides to get:

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since the value of x is a complex number, this means that there are no roots to the equation.
since the roots are when the equation crosses the x-axis, this means that this equation does not cross the x-axis.
a graph of is shown below:

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