Question

Solve the given quadratic equation by using the formula method, $x^2+8x+6=0$

Answer 1

The given quadratic equation $x^2+8x+6=0$ is in the form $a{x}^2+bx+c=0$ where $a=1,b=8$ and $c=6$.

We know that the quadratic formula is $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$, therefore, substitute $a=1,b=8$ and $c=6$ in $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$ as follows:

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{-8\pm \sqrt{8^2-(4\times 1\times 6)}}{2\times 1}=\frac{-8\pm \sqrt{64-24}}{2}$

$=\frac{-8\pm \sqrt{40}}{2}=\frac{-8\pm \sqrt{4\times 10}}{2}=\frac{-8\pm 2\sqrt{10}}{2}=\frac{2(-4\pm \sqrt{10})}{2}=-4\pm \sqrt{10}$

Hence, $x=-4+\sqrt{10}$ or $x=-4-\sqrt{10}$.