Question

# solve x^2−10x=−21x

solve $$\displaystyle{x}^{{2}}−{10}{x}=−{21}{x}$$

2020-10-22
We have to solve: solve x2−10x=−21
$$\displaystyle{x}^{{2}}-{10}{x}=-{21}\to{x}^{{2}}-{10}{x}+{21}={0}$$
For a quadratic equation of the form $$\displaystyle{a}{x}^{{2}}+{b}{x}+{c}={0}$$ the solution are $$\displaystyle\frac{{-{b}\pm\sqrt{{{b}^{{2}}-{4}{a}{c}}}}}{{2}}{a}$$
Therefore the solution of the given equation are $$\displaystyle\frac{{-{\left({10}\right)}\pm\sqrt{{{\left(-{10}\right)}^{{2}}}}-{4}\cdot{1}\cdot{21}}}{{2}}\cdot{1}=\frac{{{10}+\sqrt{{16}}}}{{2}}\cdot{1}=\frac{{{10}\pm{4}}}{{2}}={7.3}$$
Hence the solution are x=7 and x=3
2021-08-10