Question

Решите квадратные уравнения, пожалуйста
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Answer 1

Объяснение:

2).

${x}^{2} - 5x - 4 = 10$

${x}^{2} - 5x - 14 = 0$

$d = ( - 5)^{2} - 4 \times 1 \times ( - 14) = 25 + 56 = 81 \: ( {9}^{2} )$

$x1 = \frac{ - ( - 5) + 9}{2} = 7$

$x2 = \frac{ - ( - 5) - 9}{2} = - 2$

Ответ: x1 = 7; x2 = -2

4).

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

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

${x}^{2} + 3x - 4 = 0$

$d = 3^{2} - 1 \times 4 \times ( - 4) = 9 + 16 = 25 \: ( {5}^{2} )$

$x1 = \frac{ - 3 + 5}{2} = 1$

$x2 = \frac{ - 3 - 5}{2} = - 4$

Ответ: x1 = 1; x2 = -4

6).

$9x - {x}^{2} = 6 + 2x$

$9x - {x}^{2} - 6 - 2x = 0$

$- {x}^{2} + 7x - 6 = 0$

${x}^{2} - 7x + 6 = 0$

$d = ({ - 7})^{2} - 4 \times 1 \times 6 = 49 - 24 = 25 \: ( {5}^{2} )$

$x1 = \frac{7 + 5}{2} = 6$

$x2 = \frac{7 - 5}{2} = 1$

Ответ: x1 = 6; x2 = 1

8).

$x - 2 {x}^{2} + 7 = - 1 - 5x$

$x - 2 {x}^{2} + 7 + 1 + 5x = 0$

$- 2 {x}^{2} + 6x + 8 = 0$

$2 {x}^{2} - 6 - 8 = 0$

$d = ( - 6)^{2} - 4 \times 2 \times ( - 8) = 36 + 64 = 100 \: ( {10}^{2} )$

$x1 = \frac{6 + 10}{4} = 4$

$x2 = \frac{6 - 10}{4} = - 1$

Ответ: x1 = 4; x2 = -1