Solve the following equation by completing the square.?

Question

6m^2 + 5m -3 = 0

Answer 1

The equation 6m ² + 5m - 3 = 0

Separate variables and constants aside by adding 3 to each side.

6m ² + 5m  = 3

Here m ² coefficient is 6 , for perfect square make m ² coefficient 1 by dividing each side by 6.

m ² + 5m/6  = 1/2

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

m ² + 5m/6 + 25/144 = 1/2 + 25/144

(m + 5/12) ² = (72 + 25)/144

(m + 5/12) ²  = 97/144

Take square root both sides.

m + 5/12 = ± √97/144

m + 5/12 = ± √97/12

m = -5/12 ± √97/12

m = 1/12[- 5 ± √97]

Solutions are m = 1/12(- 5 + √97) and m = 1/12(- 5 - √97).