Question

1). 10-2(x-3)=4(x-3)-20 2). 3x квадрат -7х+4=0 3). 4x квадрат -10x=0 4). 3x квадрат -21=0 5). 20-(x-3)(x+4)=(2x-5) квадрат +7

Answer 1

1) 10-2(x-3)=4(x-3)-20
10-2х-6=4х-12-20
-2х-4х=-12-20-10+6
-6х=-36
х=6
2)
$3 {x}^{2} - 7x + 4 = 0 \\ d = 49 - 4 \times 4 \times 3 = 49 - 48 = 1 \\ x1 = \frac{7 + 1}{6} = \frac{4}{3} = 1 \frac{1}{3 } \\ x2 = \frac{7 - 1}{6} = 1$
3) 4x^2 -10x=0
2x(2x-5)=0
2x=0
x1=0

2x-5=0
2x=5
x2=2.5
4)3x^2-21=0
3x^2=21
x^2=7
x1=корень 7
х2= -корень 7

5)20-х^2-4х+3х+12=4х^2-20х+25+7
-4х^2-х^2+3х+20х-4x=-20+25+7-12
-5x^2+x=0
х(-5x+1)=0
х1=0
-5х=-1
х2=1/5

Answer 2

Let's solve each of the given equations step by step:

1. 10 - 2(x - 3) = 4(x - 3) - 20

Expand the brackets: 10 - 2x + 6 = 4x - 12 - 20

Combine like terms: 16 - 2x = 4x - 32

Add 2x to both sides: 16 = 6x - 32

Add 32 to both sides: 48 = 6x

Divide by 6: x = 8

Therefore, the solution to the equation is x = 8.

2. 3x^2 - 7x + 4 = 0

This is a quadratic equation. We can solve it using factoring or the quadratic formula.

Factoring method: The equation factors as: (3x - 4)(x - 1) = 0

Setting each factor equal to zero: 3x - 4 = 0 or x - 1 = 0

Solving for x: 3x = 4 or x = 1

Dividing by 3: x = 4/3 or x = 1

Therefore, the solutions to the equation are x = 4/3 and x = 1.

3. 4x^2 - 10x = 0

Factor out x: x(4x - 10) = 0

Setting each factor equal to zero: x = 0 or 4x - 10 = 0

Solving for x: x = 0 or 4x = 10

Dividing by 4: x = 0 or x = 10/4 = 5/2

Therefore, the solutions to the equation are x = 0 and x = 5/2.

4. 3x^2 - 21 = 0

Add 21 to both sides: 3x^2 = 21

Divide by 3: x^2 = 7

Taking the square root of both sides: x = ±√7

Therefore, the solutions to the equation are x = √7 and x = -√7.

5. 20 - (x - 3)(x + 4) = (2x - 5)^2 + 7

Expand the brackets: 20 - (x^2 + x - 12) = (2x - 5)^2 + 7

Simplify: 20 - x^2 - x + 12 = 4x^2 - 20x + 25 + 7

Combine like terms: -x^2 - 5x + 32 = 4x^2 - 20x + 32

Rearrange to bring all terms to one side: 5x^2 - 15x = 0

Factor out x: x(5x - 15) = 0

Setting each factor equal to zero: x = 0 or 5x - 15 = 0

Solving for x: x = 0 or 5x = 15

Dividing by 5: x = 0 or x = 15/5 = 3

Therefore, the solutions to the equation are x = 0 and x = 3.

I have solved the given equations. If you have any more questions, feel free to ask!