Question

Solve the following quadratic equation:

`x^2 + 2sqrt(2)x - 6 = 0`

Answer 1

We write:

`2sqrt(2)x = 3sqrt(2)x - sqrt(2)x` as `x^2 xx (-6) = -6x^2 = 3sqrt(2)x xx (-sqrt(2)x)` 

∴ `x^2 + 2sqrt(2)x - 6 = 0` 

⇒ `x^2 + 2sqrt(2)x - sqrt(2)x - 6 = 0` 

⇒ `x(x + 3sqrt(2)) - sqrt(2)(x + 3sqrt(2)) = 0`

⇒ `(x + 3sqrt(2))(x - sqrt(2)) = 0` 

⇒ `x + 3sqrt(2) = 0` or `x - sqrt(2) = 0` 

⇒ `x = -3sqrt(2)` or `x = sqrt(2)` 

Hence, the roots of the given equation are `-3sqrt(2)` and `sqrt(2)`.