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2x^2  - 3x  - 7  = 36      subtract 36 from both sides

2x^2  - 3x  - 43  = 0

Since the discriminant  is

(-3)^2  - (4)(2)(-43)

9  + 344

353 > 0

We wil have two real roots

2) similar here

6x^2 +12x = 48

BUT you need to have x^2 coefficient = 1    so divide through by 6

x^2 + 2x = 8      Now 'complete the square' again

x^2 + 2x +1 = 8+1

(x+1)^2  =  9

x + 1    = +- 9

x =8 or -10

1)  n^2 -18n  = 40      take 1/2 of the 'n' coefficient, square it , then add it ro both the sides of the equation

n^2 -18n + 81 = 40  + 81

(n-9)^2     = 121                        Now take sqrt of both sides

(n-9) = +- 11

n=20  or  -2

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(x-4)^2 - 28= 8         add 28 to both sides

(x - 4)^2 =8+28

(x - 4)^2 = 36            take the square root of both sides

x - 4 = +or-6

x - 4 = 6                    add 4 to both sides

x = 10 - this is one solution

x - 4 = - 6                   add 4 to both sides

x = - 6 + 4

x = - 2 - this is the 2nd solution

It has 2 solution because it is a quadratic equation!.

(x-4)^2 -28 = 8     re-arrange to look like this

(x-4)^2 = 36    now take the square root

(x-4) = + or -  sqrt(36)        <-------- TWO answers

x-4 = 6   or  -6

x= 10  or  -2 

(5x + 6)^2 + (4x)^2 = H^2

Substitute 8 for x

(5*8 + 6) + (4*8)^2 = H^2

46^2  +  32^2  = H^2

H^2 = 2,116  +  1,024

H^2 = 3,140    Take the square root of both sides.

H = Sqrt(3,140)

H = +or-  56.0357 - Use the + only in this case. 

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im pretty sure its 56

10

The nth term is given  by :

64 (1/4)^n-1

so.....the 10th term is    64 (1/4)^{10 - 1}  =  64 (1/4)⁹  = 1 / 4096

11      35   ___    875

875 / 35   = r^2

25  = r^2       take both  roots

5  = r    or  - 5  = r

So ......the missing term is   35 * (5)  = 175 

Or......the missing term is  35 (-5)  =  -175

ok thx

Its 5x+6

its kinda small,is that 5x+8?

8.  To find the missing term, we can find the constant additive, C, as

22 + C  =    34  - C        add C to both  sides.....subtract 22 from each side

2C  =  34 - 22

2C  = 12       divide both sides by 2

C  = 6

So.....the missing term is  22 +  6    = 28

9.   

1/3    2/9      4 /27......

Notice that each successive term is forund by multiplying the current term by 2/3

(First answer )

6....Definitely not.....the difference  between  the terms is not an additive/subtractive  constant

7.   

 20  16  12 

The nth term is given by

20  - 4 (n - 1)

So....the 12th  term is

20 - 4(12 - 1)  =

20 - 4(11)  =

20 - 44  =

-24