Question

Розв'яжіть рівняння: 1) 14x2-(2x-3) (7x+4)=14;2) (8x+10) (3-x)=(11-2x) (4x+5)-5;3) (x+6)(x-3)-(x+3)(x+9)=9.​

Answer 1

Ответ:

Объяснение:

1) 14x²-(2x-3) (7x+4)=14;

14x²-14x²-8x+21x+12 = 14;

13x = 2;

x=2/13.

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2) (8x+10) (3-x)=(11-2x) (4x+5)-5;

24x-8x²+30 -10x = 44x+55-8x²-10x - 5;

24x-44x = 55 - 5 -30;

-20x = 20;

x=-1.

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3) (x+6)(x-3)-(x+3)(x+9)=9.​

x²-3x+6x-18 - x²-9x-3x-27 = 9;

-3x+6x-9x-3x = 9+27+18;

-9x = 54;

x=-54/9;

x=-6.

Answer 2

Ответ:

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Answer 3

1. 14x^2 - (2x - 3)(7x + 4) = 14

Let's expand the right side and simplify the equation:

14x^2 - (2x - 3)(7x + 4) = 14

14x^2 - (14x^2 + 8x - 21x - 12) = 14

Now, distribute the negative sign into the second term:

14x^2 - 14x^2 - 8x + 21x + 12 = 14

Now, combine like terms:

-8x + 21x + 12 = 14

13x + 12 = 14

Subtract 12 from both sides:

13x = 14 - 12

13x = 2

Divide by 13:

x = 2/13

So, the solution is:

x = 2/13

2. (8x + 10)(3 - x) = (11 - 2x)(4x + 5) - 5

Let's expand and simplify the equation:

(8x + 10)(3 - x) = (11 - 2x)(4x + 5) - 5

First, expand the expressions on both sides:

(24x - 8x^2 + 30 - 10x) = (44x^2 + 55x - 22x - 10x^2) - 5

Now, combine like terms:

24x - 8x^2 + 30 - 10x = 44x^2 + (55x - 22x) - 10x^2 - 5

Now, simplify further:

24x - 8x^2 + 30 - 10x = 44x^2 + 33x - 10x^2 - 5

Combine like terms on both sides:

-8x^2 - 10x^2 - 24x + 10x - 33x + 8x^2 = -5 - 30

Now, simplify:

-18x = -35

Divide both sides by -18 to isolate x:

x = (-35) / (-18)

x = 35/18

So, the solution is:

x = 35/18

3. (x + 6)(x - 3) - (x + 3)(x + 9) = 9

Let's expand and simplify the equation:

(x + 6)(x - 3) - (x + 3)(x + 9) = 9

First, expand the expressions on both sides:

(x^2 - 3x + 6x - 18) - (x^2 + 9x + 3x + 27) = 9

Now, combine like terms:

(x^2 + 3x - 18) - (x^2 + 12x + 27) = 9

Now, distribute the negative sign on the left side:

x^2 + 3x - 18 - x^2 - 12x - 27 = 9

Now, combine like terms:

(3x - 12x) + (-18 - 27) = 9

-9x - 45 = 9

Add 45 to both sides:

-9x = 9 + 45

-9x = 54

Divide both sides by -9 to isolate x:

x = -54 / -9

x = 6

So, the solution is:

x = 6