Answer
$\text{$x-$intercepts: } \{
-5.4,-2.6 \}
$
Work Step by Step
Setting $y=0$ and solving for $x$ using $x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}$ (or the Quadratic Formula), then the $x-$intercept/s of the given equation, $
y=x^2+8x+14
,$ is/are
\begin{array}{l}\require{cancel}
x^2+8x+14=0
\\\\
x=\dfrac{-8\pm\sqrt{8^2-4(1)(14)}}{2(1)}
\\\\
x=\dfrac{-8\pm\sqrt{64-56}}{2}
\\\\
x=\dfrac{-8\pm\sqrt{8}}{2}
\\\\
x=\dfrac{-8\pm\sqrt{4\cdot2}}{2}
\\\\
x=\dfrac{-8\pm\sqrt{(2)^2\cdot2}}{2}
\\\\
x=\dfrac{-8\pm2\sqrt{2}}{2}
\\\\
x=\dfrac{2(-4\pm\sqrt{2})}{2}
\\\\
x=\dfrac{\cancel{2}(-4\pm\sqrt{2})}{\cancel{2}}
\\\\
x=-4\pm\sqrt{2}
.\end{array}
Hence, the $x-$intercepts are
\begin{array}{l}\require{cancel}
\text{$x-$intercepts: } \{
-5.4,-2.6 \}
.\end{array}