I have been doing stuff with quadratics over the last few weeks, although I find some of it hard, I have understood most of it better than all the other content I have learned over the last few months.

So, I have now been learning how to solve a quadratic equation of the form

ax^{2}+bx+c were a, b, and c are constants, if you can not factorize the equation then you can use a formula

x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}

To solve the quadratic equation x^{2}+6x+1=0 find the constants so, a=1 (because it is x^{2} b=6 and c=1.

If I sub these in to the following formula.
x=\dfrac{-b\pm\sqrt{b^{2}-4ac}}{2a}

=\dfrac{-6\pm\sqrt{6^{2}-4\times1\times1}}{2\times1}

=\dfrac{-6\pm\sqrt{36-4}}{2}

=\dfrac{-6\pm\sqrt{32}}{2} 32=16\times2

=\dfrac{-6\pm4\sqrt{2}}{2} \sqrt{32}=4\sqrt{2}

=\dfrac{-6}{2} \pm \dfrac{4\sqrt{2}}{2}=-3\pm2\sqrt{2}

so the solutions to this equation are...
x=-3+ 2\sqrt{2} and x=-3-2\sqrt{2}

I do have another quadratic equation to solve in the same sort of way, I will add that in the next couple of days. Making sure all the typesetting for the equations is correct takes a bit of time of which I have very little nowadays.