Question

Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.

Answer 1

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

Now, by using the formula x = `(-b +- sqrt(b^2 - 4ac))/(2a)`, we get

x = `(-2sqrt(2) +- sqrt((2sqrt(2))^2 - 4 xx 1 xx (-6)))/(2 xx 1)`

⇒ x = `(-2sqrt(2) +- sqrt(8 + 24))/2`

⇒ x = `(-2sqrt(2) +- 4sqrt(2))/2`

= `- sqrt(2) +- 2sqrt(2)`

⇒ x = `-sqrt(2) + 2sqrt(2)`, x = `-sqrt(2) -  2sqrt(2)`

⇒ x = `sqrt(2)`, x = `-3sqrt(2)`