For this case we have the following quadratic equation:
\(x ^ 2 = 19x + 1\)
Rewriting we have:
\(x ^ 2 - 19x - 1 = 0\)
Then, using the quadratic formula we have:
\(x =\frac{-b+/-\sqrt{b^2-4ac}}{2a}\)
Substituting values:
\(x =\frac{-(-19)+/-\sqrt{(-19)^2-4(1)(-1)}}{2(1)}\)
Rewriting:
\(x =\frac{19+/-\sqrt{361+4}}{2}\)
\(x =\frac{19+/-\sqrt{365}}{2}\)
Therefore, the solutions are given by:
\(x =\frac{19+\sqrt{365}}{2}\)
\(x =\frac{19-\sqrt{365}}{2}\)
Answer:
The solutions of the equation are:
\(x =\frac{19+\sqrt{365}}{2}\)
\(x =\frac{19-\sqrt{365}}{2}\)
