Question

Solve: ${150x}^2-750x-8=0$

Answer 1

$150x^2-750x-8=0$

$\Rightarrow 2(125x^2-375x-4)=0$

$\Rightarrow 125x^2-375x-4=0$

$\Rightarrow x^2-\frac{375}{125}x-\frac{4}{125}=0$

$\Rightarrow x^2-3x-\frac{4}{125}=0$

$\Rightarrow x^2-2x\times \frac{3}{2}+\frac{3^2}{2^2}-\frac{3^2}{2^2}-\frac{4}{125}=0$

$\Rightarrow {(x-\frac{3}{2})}^2=\frac{9}{4}+\frac{4}{125}$

$\Rightarrow {(x-\frac{3}{2})}^2=\frac{1125+16}{500}=\frac{1141‬}{500}$

$\Rightarrow x-\frac{3}{2}=\pm \sqrt{\frac{1141‬}{500}}$

$\therefore x=\frac{3}{2}\pm \frac{1}{10}\sqrt{\frac{1141‬}{5}}$