ElectricPavlov

Re-arrange to 

x^2 +12x -4 = 0     complete the square 

(x+6)^2  = 4 + 36 

x+6 = +- sqrt 40 

x =  - 6 +- sqrt 40      <==== these are the roots 

Now square the roots

(-6 + sqrt 40)² = 76 - 12 sqrt 40 

(-6  - sqrt 40)²  = 76 +12 sqrt 40

                        added together =  76 + 76 =   + 152  

Start with a list of primes > 20 

  23    29  31   37   

23 * 37 is too large 

so you have 

  23 x 29    = 667

   23 x 31   = 713 

          and that's it !     

If you start with a  3 x 3 x 3   cube   , when you cut it up there will be 

ONE cube on each face with only one painted side = six cubes with one painted side

Only the very center cube will have no painted sides 

EIGHT cubes will have THREE painted sides

TWELVE cubes will have TWO painted sides

there are 27 cubes, randomly drawing a cube:   

of the cubes you have a   6/27   chance of picking a 1 painted side                   prob of rolling paint side up = 1/6

                                          1 / 27                                zero painted side                                                          = 0/6

                                             12/27                             two painted sides                                                          = 2/6

                                               8/27                             three painted sides                                                       = 3/6 

The the total probability of a painted side up is 

             6/27 * 1/6    + 1/27 * 0/6     +   12/27 * 2/6      +   8/27 * 3/6    =   1/3 chance of painted side up 

Maybe a bit simpler : there are a total of 54 painted sides out of  162  smaller-cube sides    black =  54/162 = 1/3 

2 pi /7  R   =    2pi / 7   R *  360°/2pi R   = 51 3/7 °   

cos (2pi/7 R) = .6234898     ( Using calculator in RADIAN mode) 

cos (51 /37 °) = .6234898    ( using calculator in DEGREE mode) 

   YOUR calculator may have a different way of calculating in RADIAN or DEGREE mode, but the WEB2.0 calculator is switched between the two modes by checking one of the two buttons in the lower left corner ....

Another "need the diagram, wiseowl"    ..... 

~EP

Suprising answer below  ! 

200 kg * 95% = 190 kg of water    and 10 kg of fruit solids

then,  after two days there is   STILL 10 kg of fruit solids which now represent  10% of the total weight 

          the total weight will then be only   100 kg  !!     

For RIGHT triangles yo HAVE to learn/remember   S-O-H-C-A-H-T-O-A

S-O-H       SINE = OPPOSITE LEG / HYPOTENUSE

For angle ACB    this would be   24 / 25   

   ( you'll have to use the Pythagorean Theorem to find the length of the hypotenuse     Hypotenuse^2 = 7^2 + 24^2  )

  Here is perhaps a simler , exact - answer way:

x^2 + y^2 - 2xy = 32 

(x-y)^2 = 32 

x -y = +-  4 sqrt 2 

y =   x - 4 sqrt 2    and     x +  4sqrt 2 

then use the line quation:

x + y = 10 

x + x-  4 sqrt 2 = 10 

2x = 10 +4 sqrt 2

x = 5 +2 sqrt 2        and the other is x = 5 - 2 sqrt 2    Then the corresponding 'y' s are 

y=  5 - 2 sqrt 2        and                          5 + 2 sqrt2                                                                   

  Same answers....just maybe easier...and exact.   

Need the original side length......missing in your post....