x^2+3x-1=0 by completing the square

Question

by completing the square.

Answer 1

x² + 3x - 1= 0

Separate variables and constants aside by adding 1 to each side.

x² + 3x = 1

 To change the expression into a perfect square trinomial add (half the x coefficient)² to each side of the expression.

 Here x coefficient = 3. so, (half the x coefficient)² = (3/2)²= 9/4.

Add 9/4 to each side

x² + 3x + 9/4= 1+ 9/4

(x + 3/2)²= (4+9)/4

(x + 3/2)²= 13/4

Take square root both sides

x + 3/2 = ±√(13/4)

x + 3/2 = ±√13/2

x = -3/2 ± √13/2

x = -3/2+√13/2 and x = -3/2-√13/2

Solution x = (-3+√13)/2

x = (-3-√13)/2.