Answer
No real number solutions
Work Step by Step
Step 1: Comparing $x^{2}-2x+6=0$ to the standard form of a quadratic equation $ax^{2}+bx+c=0$, we obtain:
$a=1$, $b=-2$ and $c=6$
Step 2: The quadratic formula is:
$x=\frac{-b \pm \sqrt {b^{2}-4ac}}{2a}$
Step 3: Substituting the values of a, b and c in the formula:
$x=\frac{-(-2) \pm \sqrt {(-2)^{2}-4(1)(6)}}{2(1)}$
Step 4: $x=\frac{2\pm \sqrt {4-24}}{2}$
Step 5: $x=\frac{2 \pm \sqrt {-20}}{2}$
Since their are no real number solutions to $ \sqrt {-20}$, there are no real number solutions to the equation.
