Solution for Problem 1.3.1

 
Solve for x: 8x2 + 2x = 0

Solve

Step
8x2 + 2x = 0 Factor, if possible.
2x(4x + 1) = 0 Zero Property of Multiplication

2x = 0 or 4x + 1 = 0

 If ab = 0 then a = 0 or b = 0
2x = 0 gives x = 0/2 = 0 Solve each linear equation separately
or 
4x + 1 = 0 gives 4x = -1 
x = -1/4
{-1/4, 0} Solution Set Notation

Solve

If x = 0, then
8(0)2 + 2(0) = 0  
    0 + 0 = 0 

If x = -1/4, then
8(-1/4)2 + 2(-1/4) = 0  
    8(1/16) – 2/4 = 0 
1/2 – 1/2 =