#2**+1 **

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 **

Guest Dec 8, 2019