Solution for Problem 1.3.5

 Solve for x:  Solve for x:  x2 + 6x – 1 = 0    Completing the Square

Solve

Step

x2 + 6x – 1 = 0

Add 1 to both sides

x2 + 6x      = 1

x2 + 6x + (6/2)2  = 1 + (6/2)2

Take half of 6, square it, add it to both sides

(x + 3)2  = 10

Complete Square

Subtract 3 from both sides


(Exact)

Approximations...
x ≈ -3 + 3.1623  = 0.1623
x ≈ -3 – 3.1623 = -6.1623

Check 

If x  = 0.1623, then 
(0.1623)2 + 6(0.1623) – 1 = 0
 0.026341 + 0.9738 – 1 = 0
 0.0001 ≈ 0   

If x  = -6.1623, then 
(-6.1623)2 + 6(-6.1623) – 1 = 0
  37.973941 – 36.9738 – 1 = 0
 0.0001 ≈ 0