Solve for a:
a^3 - a^2 = 4624
Subtract 4624 from both sides:
a^3 - a^2 - 4624 = 0
The left hand side factors into a product with two terms:
(a - 17) (a^2 + 16 a + 272) = 0
Split into two equations:
a - 17 = 0 or a^2 + 16 a + 272 = 0
Add 17 to both sides:
a = 17 or a^2 + 16 a + 272 = 0
Subtract 272 from both sides:
a = 17 or a^2 + 16 a = -272
Add 64 to both sides:
a = 17 or a^2 + 16 a + 64 = -208
Write the left hand side as a square:
a = 17 or (a + 8)^2 = -208
Take the square root of both sides:
a = 17 or a + 8 = 4 i sqrt(13) or a + 8 = -4 i sqrt(13)
Subtract 8 from both sides:
a = 17 or a = 4 i sqrt(13) - 8 or a + 8 = -4 i sqrt(13)
Subtract 8 from both sides:
a = 17
