equations

Solve for X over the real numbers:
X^2+3 X-1 = 0

Add 1 to both sides:
X^2+3 X = 1

Add 9/4 to both sides:
X^2+3 X+9/4 = 13/4

Write the left hand side as a square:
(X+3/2)^2 = 13/4

Take the square root of both sides:
X+3/2 = sqrt(13)/2 or X+3/2 = -sqrt(13)/2

Subtract 3/2 from both sides:
X = sqrt(13)/2-3/2 or X+3/2 = -sqrt(13)/2

Subtract 3/2 from both sides:
Answer: | 
| X = sqrt(13)/2-3/2 or X = -3/2-sqrt(13)/2

You could also just use the quadratic equation :))