complete the square: 6x^2+11x+3=0

Question

Have to Complete the square.

Answer 1

6x² + 11x + 3 = 0

Divide each side by 6.

x² + 11/6x + 3/6 = 0

Separate variables and constants aside by subtracting 1/2 from each side.

x² + 11/6x = - 1/2

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

 Here x coefficient = 11/6. so, (half the x coefficient)² = (11/12)²= 121/144.

Add 121/144 to each side.

x² + 11/6x + 121/144 = - 1/2 + 121/144

(x + 11/12)²= 49/144

Take square root both sides.

x + 11/12 = ± 7/12

x = -11/12 ± 7/12

x = - 1/3,- 9/2.

 

Comments

x = -11/12 ± 7/12

x = -11/12 - 7/12  and  x = -11/12 + 7/12

x = -18/12  and  x = -4/12

x = - 3/2, - 1/3.