Решить уравнения: 1) 10 x^{2} + 5 х=02) 12 x^{2} + 3 х=03) 25-100 x^{2} = 04) 4-36 x^{2} = 05) 2 x^{2} - 14=0

Найдем корни.

1) 10 * x^2 + 5 * х = 0;

Вынесем за скобки общий множитель.

5 * x * (2 * x + 1) = 0;

{ 5 * x = 0;

2 * x + 1 = 0;

{ x = 0;

2 * x = - 1;

{ x = 0;

x = - 1/2;

{ x = 0;

x = - 0.5.

2) 12 * x^2 + 3 * х = 0;

3 * x * (4 * x + 1) = 0;

{ x = 0;

4 * x + 1 = 0;

{ x = 0;

4 * x = - 1;

{ x = 0;

x = - 1/4;

{ x = 0;

x = - 0.25.

3) 25 - 100 * x^2 = 0;

5^2 - (10 * x) ^2 = 0;

(5 - 10 * x) * (5 + 10 * x) = 0;

{ 5 - 10 * x = 0;

5 + 10 * x = 0;

{ 10 * x = 5;

10 * x = - 5;

{ x = 5/10;

x = - 5/10;

{ x = 0.5;

x = - 0.5.

4) 4 - 36 * x^2 = 0;

(2 - 6 * x) * (2 + 6 * x) = 0;

{ 6 * x = 2;

6 * x = - 2;

{ x = 1/3;

x = - 1/3.

5) 2 * x^{2} - 14 = 0;

2 * x^2 = 14;

x^2 = 7;

x = + 7^0.5;

x = - 7^0.5.