$$a+b=-26$$ $$ab=5\times 5=25$$

$$-1,-25$$ $$-5,-5$$

$$-1-25=-26$$ $$-5-5=-10$$

$$a=-25$$ $$b=-1$$

$$\left(5x^{2}-25x\right)+\left(-x+5\right)$$

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

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

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

$$5x^{2}-26x+5=0$$

$$x=\frac{-\left(-26\right)±\sqrt{\left(-26\right)^{2}-4\times 5\times 5}}{2\times 5}$$

$$x=\frac{-\left(-26\right)±\sqrt{676-4\times 5\times 5}}{2\times 5}$$

$$x=\frac{-\left(-26\right)±\sqrt{676-20\times 5}}{2\times 5}$$

$$x=\frac{-\left(-26\right)±\sqrt{676-100}}{2\times 5}$$

$$x=\frac{-\left(-26\right)±\sqrt{576}}{2\times 5}$$

$$x=\frac{-\left(-26\right)±24}{2\times 5}$$

$$x=\frac{26±24}{2\times 5}$$

$$x=\frac{26±24}{10}$$

$$x=\frac{50}{10}$$

$$x=5$$

$$x=\frac{2}{10}$$

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

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

$$5x^{2}-26x+5=0$$

$$5x^{2}-26x+5-5=-5$$

$$5x^{2}-26x=-5$$

$$\frac{5x^{2}-26x}{5}=-\frac{5}{5}$$

$$x^{2}-\frac{26}{5}x=-\frac{5}{5}$$

$$x^{2}-\frac{26}{5}x=-1$$

$$x^{2}-\frac{26}{5}x+\left(-\frac{13}{5}\right)^{2}=-1+\left(-\frac{13}{5}\right)^{2}$$

$$x^{2}-\frac{26}{5}x+\frac{169}{25}=-1+\frac{169}{25}$$

$$x^{2}-\frac{26}{5}x+\frac{169}{25}=\frac{144}{25}$$

$$\left(x-\frac{13}{5}\right)^{2}=\frac{144}{25}$$

$$\sqrt{\left(x-\frac{13}{5}\right)^{2}}=\sqrt{\frac{144}{25}}$$

$$x-\frac{13}{5}=\frac{12}{5}$$ $$x-\frac{13}{5}=-\frac{12}{5}$$

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

$$x ^ 2 -\frac{26}{5}x +1 = 0$$

$$r + s = \frac{26}{5} $$ $$ rs = 1$$

$$r = \frac{13}{5} - u$$ $$s = \frac{13}{5} + u$$

$$(\frac{13}{5} - u) (\frac{13}{5} + u) = 1$$

$$\frac{169}{25} - u^2 = 1$$

$$-u^2 = 1-\frac{169}{25} = -\frac{144}{25}$$

$$u^2 = \frac{144}{25}$$ $$u = \pm\sqrt{\frac{144}{25}} = \pm \frac{12}{5} $$

$$r =\frac{13}{5} - \frac{12}{5} = 0.200$$ $$s = \frac{13}{5} + \frac{12}{5} = 5$$