Hi Katherine,
We have the equation
x + 49/x = 14
The first thing I would do is multiply all terms by x. This will give us
x2 + 49 = 14x
Let's bring the 14x to the left side of the equation so the equation equals zero. To do this, subtract 14x.
x2 - 14x + 49 = 0
Next we need to factor this equation.
When factoring the first thing I look at is the sign of the constant, in this cast +49. Since the sign is positive, this tells me that the factors have the same sign. I just don't know if it's plus or minus. I know it's minus by looking at the sign of the x term (-14x).
So we have
(x-___)(x-___) = 0
To fill in those blanks, I have to think of two integers, which when multiplied together will gives +49 and when added together will yield -14.
(-7)(-7) = 49 and -7+(-7) = -14 will satisfy this requirement.
(x-7)(x-7) = 0
Set each factor = 0
x-7=0
and solve,
x = 7
