Question

Solve the following quadratic equation by completing the square method.

 2y² + 9y + 10 = 0

Answer 1

2y² + 9y +10 = 0 

`y^2 + 9/2y + 5 = 0`   ...[Dividing both sides by 2]

If `y2 + 9/2y + k = (y + a)^2`, then

`y^2 + 9/2y + k = y^2 + 2ay + a^2`

Comparing the coefficients, we get

`9/2 = 2a and k = a^2`

∴ `a = 9/4 and k = (9/4)^2 = 81/16`

Now, `y^2 + 9/2y + 5 = 0`

∴ `y^2 + 9/2y + 81/16 - 81/16 + 5 = 0`

∴ `(y + 9/4)^2 + ((-81 + 80)/16) = 0`

∴ `(y + 9/4)^2 - 1/16 = 0`

∴ `(y + 9/4)^2 = 1/16`

Taking the square root of both sides, we get

`y + 9/4 = ± 1/4`

∴ `y + 9/4 = 1/4 or y + 9/4 = -1/4`

∴ `y = 1/4 - 9/4 or y = -1/4 - 9/4`

∴ `y = (-8)/4 = -2 or y = -10/4 = (-5)/2`

∴ The roots of the given quadratic equation are −2 and `(-5)/2`.