Question

Solve: x²+250x-7500000.

Answer 1

These are the most accurate values of x,if the equation is x²+250x-7500000=0

Answer 2

quadratic eq  :    x² + 250 x - 7500, 000 = 0
discriminant:   b² - 4ac = √(250² + 4*1*7500,000) 
                                    = 250 √(1 + 16*30) = 250*√481

x = [- 250 + 250√481]/2   or  [-250 - 250√481]/2
  = 125(√481  - 1)    or    -125(√481 +1)
  = 125 [√(484 - 3)  -1 ]   or    -125 * [√(484 -3)  + 1 ]
  ≈ 125 [ 22 √(1 - 3/484)  - 1]  or   -125 [ 22 √(1 -3/484)  + 1 ]
  ≈ 125 [ 22 (1 - 3/968)  - 1 ]   or   -125 [ 22 (1 - 3/968)  + 1]
  ≈ 125 [ 22 - 3/44  - 1]     or   -125 [ 22 - 3/44 + 1 ]
  ≈ 125 * 921/44    or   - 125 * 1011/44
  ≈ 921000/352      or    - 1011000/352

near exact solution:  x = 2, 616.464     or    - 2, 866.464