How do you solve x(x-4)-2=43?

Mar 27, 2015

I would start by multiplying the $x$ to get rid of the bracket:
${x}^{2} - 4 x - 2 = 43$
rearranging:
${x}^{2} - 4 x - 2 - 43 = 0$
${x}^{2} - 4 x - 45 = 0$
so that:
${x}_{1 , 2} = \frac{4 \pm \sqrt{16 - 4 \left(1 \cdot - 45\right)}}{2} = \frac{4 \pm \sqrt{196}}{2} = \frac{4 \pm 14}{2}$
So, you get two solutions:
${x}_{1} = \frac{18}{2} = 9$
${x}_{2} = - \frac{10}{2} = - 5$

:-)