How do you solve #30 + x − x^2 = 0#?
Invert (multiply by -1, has the same solutions) and complete the square:
Ans: -5 and 6
I use the new Transforming Method (Google, Yahoo, Bing Search)
Find 2 numbers knowing sum (1) and product (-30). Roots have opposite signs since a and c have opposite signs.
Factor pairs of (-30) --> (-2, 15)(-4, 5)(-5, 6). This sum is 1 = b.
Since a < 0. then the 2 real roots are: -5 and 6.
You could use the quadratic formula.
First, rewrite your quadratic in the form
for which the quadratic formula takes the form
You will start from
which can be rewritten as
In this case,
The two solutions to this quadratic equation will thus be