10x²+5x=0 x-x²=0 6x²+24x=0 x²-25=0

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вопрос

To solve each of these equations for x, we need to factor out x or x² and set each factor equal to 0.

1) 10x² + 5x =
Factor out x: x(10x + 5) =
Set each factor equal to 0
x = 0 or 10x + 5 =
Solve for x: x = 0 or 10x = -5, x = -5/10, x = -1/2

2) x - x² =
Factor out x: x(1 - x) =
Set each factor equal to 0
x = 0 or 1 - x =
Solve for x: x = 0 or x = 1

3) 6x² + 24x =
Factor out 6x: 6x(x + 4) =
Set each factor equal to 0
6x = 0 or x + 4 =
Solve for x: x = 0 or x = -4

4) x² - 25 =
Factor as the difference of squares: (x + 5)(x - 5) =
Set each factor equal to 0
x + 5 = 0 or x - 5 =
Solve for x: x = -5 or x = 5

Therefore, the solutions for each equation are
1) x = 0, -1/
2) x = 0,
3) x = 0, -
4) x = -5, 5