Question

Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2)` = 0 by the method of completing the square?

Options

• `1/8`

• `1/64`

• `1/4`

• `9/64`

Answer 1

`1/64`

Explanation:

Given equation is `9x^2 + 3/4x - sqrt(2)` = 0

`(3x)^2 + 1/4 (3x) - sqrt(2)` = 0

On putting `3x = y`

We have `y^2 + 1/4y - sqrt(2)` = 0

`y^2 + 1/4y + (1/8)^2 - (1/8)^2 - sqrt(2)` = 0

`(y + 1/8)^2 = 1/64  + sqrt(2)`

`(y + 1/8)^2 = (1 + 64 sqrt(2))/64`

Thus, `1/64` must be added and subtracted to solve the given equation.