Question

Solve quadratic equation by factorization method:

$x {}^{2} + 2 \sqrt{2} x - 6 = 0$

Answer 1

$x^{2} + 2 \sqrt{2} x - 6 = 0$

Rewrite 2√2 as (3√2 - √2) :

$x^{2} + (3 \sqrt{2} - \sqrt{2}) x - 6 = 0$

Spilt the term:

$x^{2} + 3\sqrt{2} x - \sqrt{2} x - 6 = 0$

Factorise:

$x( x + 3\sqrt{2} ) - \sqrt{2} (x + 3\sqrt{2}) = 0$

$(x - \sqrt{2})( x + 3\sqrt{2} ) = 0$

Apply zero product property:

$(x - \sqrt{2}) = 0 \ or \ ( x + 3\sqrt{2})=0$

$x = \sqrt{2} \ or \ x = - 3\sqrt{2}$