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