Question

1.1)x2 + 30x = 0;2) 10x2 + 960x = 0;3) 2,5x2 - 10 = 0;4) x2 = 0;5) -x2 + 1! = 0;6) - 0,75x2 + 1,5x = 0;7) x2 + 196 = 0;8) - 7,87x2 = 0.1) 53x2 = 0;2) x2 - 9 = 0;3) 3x2 + 57x = 0;4) x2 + 45 = 0;5) - 0,37x2 = 0;6)x2 - 11,375x = 0;7) - x2 + 3Error! = 0;8) - 0,125x2 + 0,25x = 0.Лучше с объяснениями

Answer 1

Ответ:

1)X+2+30x=0

2X+30=0

32X=0

X=0

2)10х*2+960x=0

20х+960х=0

980х=0

х=0

3)2.5х*2-10=0

5х-10=0

5х=10

х=2

4)х*2=0

2х=0

х=0

5)-х*2+1=0

-2х+1=0

-2х=0

х=1/2

6)-0.75*2+1.5х=0

-1.5х+1.5х=0

0=0

х∈R

7)х*2+196=0

2х+196=0

2х=-196

х=-98

8)х*2+196=0

2х+196=0

2х=-196

х=-98

8-7.87х*2=0

-15.74х=0

х=0

9)53х*2=0

16х=0

Х=0

10)х*2-9=0

2х-9=0

2х=9

х=9/2

11)3х*2+57х=0

6х+57=0

63х=0

х=0

12)х*2+45=0

2х+45=0

2х=-45

х=- 45/2

13)-0.37*2=0

-0.74х=0

х=0

13)х*2-11.375х=0

2х=11.375х=0

-9.375х=0

х=0

14)-х*2+3=0

-2х+3=0

-2х=-3

х=3/2

15)-0.125х*2+25х=0

-0.25х+0.25х=0

0=0

х∈R

*=умножение /=столбик

Answer 2

1. x2 + 30x = 0
Factor out x: x(x+30) = 0
Therefore, either x = 0 or x+30 = 0, so x can be either 0 or -30.

2. 10x2 + 960x = 0
Factor out 10x: 10x(x+96) = 0
Therefore, either x = 0 or x+96 = 0, so x can be either 0 or -96.

3. 2.5x2 - 10 = 0
Add 10 to both sides: 2.5x2 = 10
Divide both sides by 2.5: x2 = 4
Therefore, x can be either 2 or -2.

4. x2 = 0
Take the square root of both sides: x = 0.

5. -x2 + 1 = 0
Add x2 to both sides: 1 = x2
Take the square root of both sides: x = 1 or x = -1.

6. -0.75x2 + 1.5x = 0
Factor out x: x(-0.75x + 1.5) = 0
Therefore, either x = 0 or -0.75x + 1.5 = 0, so x can be either 0 or 2.

7. x2 + 196 = 0
This equation cannot be solved over the real numbers, since the square of any real number is non-negative. Therefore, there are no real solutions to this equation.

8. -7.87x2 = 0
Divide both sides by -7.87: x2 = 0
Therefore, x = 0.

9. 53x2 = 0
Divide both sides by 53: x2 = 0
Therefore, x = 0.

10. x2 - 9 = 0
Add 9 to both sides: x2 = 9
Take the square root of both sides: x = 3 or x = -3.

11. 3x2 + 57x = 0
Factor out 3x: 3x(x+19) = 0
Therefore, either x = 0 or x+19 = 0, so x can be either 0 or -19.

12. x2 + 45 = 0
This equation cannot be solved over the real numbers, since the square of any real number is non-negative. Therefore, there are no real solutions to this equation.

13. -0.37x2 = 0
Divide both sides by -0.37: x2 = 0
Therefore, x = 0.

14. x2 - 11.375x = 0
Factor out x: x(x-11.375) = 0
Therefore, either x = 0 or x-11.375 = 0, so x can be either 0 or 11.375.

15. -x2 + 3 = 0
Add x2 to both sides: 3 = x2
Take the square root of both sides: x = sqrt(3) or x = -sqrt(3).

16. -0.125x2 + 0.25x = 0
Factor out x: x(-0.125x+0.25) = 0
Therefore, either x = 0 or -0.125x+0.25 = 0, so x can be either 0 or 2.