For this case we have the following polynomial:
[tex] x ^ 2 = -11x + 4
[/tex]
Rewriting the polynomial we have:
[tex] x ^ 2 + 11x - 4 = 0
[/tex]
From here, we can solve the polynomial using the quadratic equation
We have then:
[tex] x=\frac{-b+/-\sqrt{b^2-4ac}}{2a} [/tex]
[tex] x=\frac{-11+/-\sqrt{11^2-4(1)(-4)}}{2(1)} [/tex]
[tex] x=\frac{-11+/-\sqrt{11^2+16}}{2} [/tex]
[tex] x=\frac{-11+/-\sqrt{121+16}}{2}
[/tex]
[tex] x=\frac{-11+/-\sqrt{137}}{2}
[/tex]
Therefore, the solutions are:
[tex] x=\frac{-11+\sqrt{137}}{2}
[/tex]
[tex] x=\frac{-11-\sqrt{137}}{2}
[/tex]
