$$a+b=3$$ $$ab=5\left(-2\right)=-10$$

$$-1,10$$ $$-2,5$$

$$-1+10=9$$ $$-2+5=3$$

$$a=-2$$ $$b=5$$

$$\left(5x^{2}-2x\right)+\left(5x-2\right)$$

$$x\left(5x-2\right)+5x-2$$

$$\left(5x-2\right)\left(x+1\right)$$

$$x=\frac{2}{5}$$ $$x=-1$$

$$5x^{2}+3x-2=0$$

$$x=\frac{-3±\sqrt{3^{2}-4\times 5\left(-2\right)}}{2\times 5}$$

$$x=\frac{-3±\sqrt{9-4\times 5\left(-2\right)}}{2\times 5}$$

$$x=\frac{-3±\sqrt{9-20\left(-2\right)}}{2\times 5}$$

$$x=\frac{-3±\sqrt{9+40}}{2\times 5}$$

$$x=\frac{-3±\sqrt{49}}{2\times 5}$$

$$x=\frac{-3±7}{2\times 5}$$

$$x=\frac{-3±7}{10}$$

$$x=\frac{4}{10}$$

$$x=\frac{2}{5}$$

$$x=-\frac{10}{10}$$

$$x=-1$$

$$x=\frac{2}{5}$$ $$x=-1$$

$$5x^{2}+3x-2=0$$

$$5x^{2}+3x-2-\left(-2\right)=-\left(-2\right)$$

$$5x^{2}+3x=-\left(-2\right)$$

$$5x^{2}+3x=2$$

$$\frac{5x^{2}+3x}{5}=\frac{2}{5}$$

$$x^{2}+\frac{3}{5}x=\frac{2}{5}$$

$$x^{2}+\frac{3}{5}x+\left(\frac{3}{10}\right)^{2}=\frac{2}{5}+\left(\frac{3}{10}\right)^{2}$$

$$x^{2}+\frac{3}{5}x+\frac{9}{100}=\frac{2}{5}+\frac{9}{100}$$

$$x^{2}+\frac{3}{5}x+\frac{9}{100}=\frac{49}{100}$$

$$\left(x+\frac{3}{10}\right)^{2}=\frac{49}{100}$$

$$\sqrt{\left(x+\frac{3}{10}\right)^{2}}=\sqrt{\frac{49}{100}}$$

$$x+\frac{3}{10}=\frac{7}{10}$$ $$x+\frac{3}{10}=-\frac{7}{10}$$

$$x=\frac{2}{5}$$ $$x=-1$$

$$x ^ 2 +\frac{3}{5}x -\frac{2}{5} = 0$$

$$r + s = -\frac{3}{5} $$ $$ rs = -\frac{2}{5}$$

$$r = -\frac{3}{10} - u$$ $$s = -\frac{3}{10} + u$$

$$(-\frac{3}{10} - u) (-\frac{3}{10} + u) = -\frac{2}{5}$$

$$\frac{9}{100} - u^2 = -\frac{2}{5}$$

$$-u^2 = -\frac{2}{5}-\frac{9}{100} = -\frac{49}{100}$$

$$u^2 = \frac{49}{100}$$ $$u = \pm\sqrt{\frac{49}{100}} = \pm \frac{7}{10} $$

$$r =-\frac{3}{10} - \frac{7}{10} = -1$$ $$s = -\frac{3}{10} + \frac{7}{10} = 0.400$$