10. x^2 + 12x + 36 = 0

10. $x^2 + 12x + 36 = 0$ $(x + 6)^2 = 0$ $x = -6$ 11. $x^2 + 5x - 6 = 0$ По теореме Виета: $x_1 + x_2 = -5$, $x_1 \cdot x_2 = -6$. Корни: $x_1 = -6, x_2 = 1$. 12. $2x^2 - 3x - 5 = 0$ $D = (-3)^2 - 4 \cdot 2 \cdot (-5) = 9 + 40 = 49 = 7^2$ $x = \frac{3 \pm 7}{4}$ $x_1 = 2,5, x_2 = -1$ 13. $7x^2 - 2x + 48 = 0$ $D = (-2)^2 - 4 \cdot 7 \cdot 48 = 4 - 1344 = -1340$ Дискриминант меньше нуля, действительных корней нет. 14. $6x(2x + 1) = 5x + 1$ $12x^2 + 6x - 5x - 1 = 0$ $12x^2 + x - 1 = 0$ $D = 1^2 - 4 \cdot 12 \cdot (-1) = 1 + 48 = 49 = 7^2$ $x = \frac{-1 \pm 7}{24}$ $x_1 = \frac{6}{24} = 0,25, x_2 = \frac{-8}{24} = -\frac{1}{3}$ 15. $x(x - 5) = 1 - 4x$ $x^2 - 5x + 4x - 1 = 0$ $x^2 - x - 1 = 0$ $D = (-1)^2 - 4 \cdot 1 \cdot (-1) = 1 + 4 = 5$ $x = \frac{1 \pm \sqrt{5}}{2}$