Answer
$x=${$2- 2i\sqrt 2,2+2i\sqrt 2$}
Work Step by Step
Given: $x^2+10=2(2x-1)$
Re-write the given equation as: $x^2+10=4x-2$
This implies that $x^2-4x+12=0$
Factorize the expression with the help of quadratic formula. Quadratic formula suggests that $x=\dfrac{-b \pm \sqrt{b^2-4ac}}{2a}$
This implies that $x=\dfrac{-(-4) \pm \sqrt{(-4)^2-4(1)(12)}}{2(1)}$
or, $x=\dfrac{4 \pm \sqrt {-32}}{2}$
or, $x=${$\dfrac{4- 4i\sqrt 2}{2},\dfrac{4+ 4i\sqrt 2}{2}$}
Hence, our solution set is: $x=${$2- 2i\sqrt 2,2+2i\sqrt 2$}
