[tex]\boxed{x_{1}=1+6i} \\ \\ \boxed{x_{2}=1-6i}[/tex]
Since we need to write the roots in the simplest form:
[tex]a+bi[/tex]
It is obvious that the roots are complex. To solve this, let's use the quadratic formula. For the Standard Equation:
[tex]ax^2+bx+c=0[/tex]
The Quadratic Formula is:
[tex]x=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\ Here: \\ \\ x^2-2x+37=0 \\ \\ So: \\ a=1 \\ b=-2 \\ c=37 \\ \\ x=\frac{-(-2)\pm \sqrt{(-2)^2-4(1)(37)}}{2(1)} \\ \\ x=\frac{2\pm \sqrt{4-148}}{2} \\ \\ x=\frac{2\pm \sqrt{-144}}{2} x=\frac{2\pm \sqrt{-1}\sqrt{144}}{2} \\ \\ x=\frac{2\pm 12\sqrt{-1}}{2} \\ \\ but \ \sqrt{-1}=i \\ \\ Two \ solutions: \\ \\ x_{1}=\frac{2+12i}{2} \\ \\ \boxed{x_{1}=1+6i} \\ \\ x_{2}=\frac{2-12i}{2} \\ \\ \boxed{x_{2}=1-6i}[/tex]
Real Roots: https://brainly.com/question/13740312#
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