Solution for Problem 1.6.1

Solve for x:  36x3 – 64x = 0  

Solve

Step
36x3 – 64x = 0  Try factoring.  It usually is the easiest method.
4x(9x2 – 16) = 0  LCM = 4x
4x(3x – 4)(3x + 4) = 0 Keeping factoring.  Difference of Squares
4x = 0 or 3x – 4 = 0 or 
3x + 4 = 0		 Set each factor to zero
x = 0 , x = 4/3 or x = -4/3 Done

Check

If x  = 0, then
36(0)3 – 64(0) = 0
    0  – 0 = 0

If x  = 4/3, then
36(4/3)3 – 64(4/3) = 0
    36(64/27)  – 64(4/3) = 0
256/3  – 256/3 = 0
   0 = 0

If x  = -4/3, then
36(-4/3)3 – 64(-4/3) = 0
    36(-64/27)  – 64(-4/3) = 0
-256/3  + 256/3 = 0
   0 = 0