Answer
$x = 3 \pm \sqrt {2}$
Work Step by Step
Write the equation in standard form:
$$x^2-6x+7=0$$
We are asked to solve this equation using the quadratic formula, which is given by:
$x = \dfrac{-b \pm \sqrt {b^2 - 4ac}}{2a}$
where $a$ is the coefficient of the $x^2$ term, $b$ is the coefficient of the 1st degree term, and $c$ is the constant.
The equation above has $a=1, b=-6,$ and $c=7$. Substitute these values into the quadratic formula to obtain:
$x = \dfrac{-(-6) \pm \sqrt {(-6)^2 - 4(1)(7)}}{2(1)}$
$x = \dfrac{6 \pm \sqrt {36 - 28}}{2}$
$x = \dfrac{6 \pm \sqrt {8}}{2}$
Since $8=4(2)$, then the expression above simplifies to:
$x = \dfrac{6 \pm\sqrt {4(2)}}{2}$
$x = \dfrac{6 \pm\sqrt {2}}{2}$
Divide numerator and denominator by $2$ to simplify this fraction:
$x = 3 \pm \sqrt {2}$
