Math Olympiad| Solve for x| Algebra

[@RyanLewis-Johnson-wq6xs]

You put down excellent variables and numbers Thank you.

[@عبدالواسع-س8م]

Thanks a lot.

[@shamilhussen5862]

The way you are doing math too appreciate me, so I love you and your job as you have hasband

[@RyanLewis-Johnson-wq6xs]

1000(x+1)^5+x^2+2x+1=0 x=-1.1=-11/10 x=-1 x=-0.95 ± 0.05Sqrt[3]i=(-19 ± Sqrt[3]i)/20

[@francisamewode233]

Thank you beautiful lady for the presentation.

[@NahidaItani]

Still 2 complex conjugate roots .

[@gabrielomorotionmwan6994]

x is real.. -1 is a real solution to the cube root of -1/1000. other two values are complex....

[@key_board_x]

@ 2:30 / 4:32
1000.(x + 1)³ + 1 = 0
10³.(x + 1)³ + 1³ = 0
[10.(x + 1)]³ + 1³ = 0 → recall: a³ + b³ = (a + b).(a² - ab + b²)
[10.(x + 1) + 1].[{10.(x + 1)}² - {10.(x + 1) * 1} + 1²] = 0
[10x + 10 + 1].[10².(x + 1)² - 10.(x + 1) + 1] = 0
[10x + 11].[100x² + 200x + 100 - 10x - 10 + 1] = 0
(10x + 11).(100x² + 190x + 91) = 0
First case: [10x + 11] = 0
10x + 11 = 0
10x = - 11
→ x = - 11/10
Second case: [100x² + 190x + 91] = 0
100x² + 190x + 91 = 0
Δ = 190² - (4 * 100 * 91) = 36100 - 36400 = - 300 ← you stop here, or continue with complex numbers

[@boubkeurkaaoiass8246]

Why did you put -1 out of the root cube on right side?

[@lwandomakaula3574]

Is this really a math Olympiad problem ?