Answer
$x = 4 ± \sqrt {10}$
Work Step by Step
Let's rewrite this equation so all the terms are on the left side of the equation and the equation equals $0$. The rewritten equation is:
$x^2 - 8x + 6 = 0$
We cannot factor this polynomial, so we need to resort to using the quadratic formula, which is given by:
$x = \frac{-b ± \sqrt {b^2 - 4ac}}{2a}$ where $a$ is the coefficient of the first term, $b$ is the coefficient of the 1st degree term, and $c$ is the constant.
Let's plug in the numbers into the formula with $a=1, b=-8, c=6$:
$x = \dfrac{-(-8) ± \sqrt {(-8)^2 - 4(1)(6)}}{2(1)}$
Simplify:
$x = \dfrac{8 ± \sqrt {64 - 24}}{2}$
Simplify what is inside the radical:
$x = \dfrac{8 ± \sqrt {40}}{2}$
The number $40$ can be expanded into the factors $4$ and $10$:
$x = \dfrac{8 ± \sqrt {(4)(10)}}{2}$
We can take out the $4$ because the square root of $4$ is $2$.
Take the square root of $4$ so we can remove it from under the radical sign:
$x = \dfrac{8 ± 2\sqrt {10}}{2}$
We divide both numerator and denominator by the factor $2$ to simplify this fraction:
$x = 4 ± \sqrt {10}$
The solution is $x = 4 ± \sqrt {10}$.
