Solution for Problem 1.3.2

Solve for x:   2x2 – 4x – 3 = 0    Quadratic Formula

ax2 + bx + c = 0

Solve

Step

a = 2, b = -4, c = -3

Identify coefficients

Substitute values for a, b , and c.  Then simplify.
There are 2 distinct answers.

     

Approximations...
x » (2 + 3.16228)/ 2 = 2.58114
  x » (2 – 3.16228)/ 2 = -0.58114

Check 

If x  = 2.58114, then
2(2.58114)2 – 4(2.58114) – 3 = 0
    13.32457 – 10.32456 – 3 = 0
0.00001 » 0  
**Rounding error

If x  = -0.58114, then 
2(-0.58114)2 – 4(-0.58114) – 3 = 0
  0.67545 + 2.32456 –  3 = 0
 0.00001 » 0   
**Rounding error