Question

find roots by spilting the middle term​

Answer 1

$x {}^{2} + 2 \sqrt{2} x - 6 = 0 \\ 6 \: is \: split \: into \: + 3 \sqrt{2 \: } \: and \: - \sqrt{2} \\ x \ {}^{2} + 3 \sqrt{2} x - \sqrt{2} - 6 = 0 \\ x(x + 3 \sqrt{2} ) - \sqrt{2} (x + 3 \sqrt{2} ) = 0 \\ (x - \sqrt{2} )(x + 3 \sqrt{2} ) = 0 \\ x - \sqrt{2} = 0 \: \: \: \: \: \: \: or \: \: \: \: \: x + 3 \sqrt{2 } = 0 \\ x = \sqrt{2} \: \: \: \: \: \: \: \: \: \: \: \: \: or \: \: \: \: \: \: \: \: \: \: \: \: x = - 3 \sqrt{2}$

Answer 2

SOLUTION:-

${x}^{2} + 2 \sqrt{2} x - 6 = 0 \\ \\ = > {x}^{2} + 3 \sqrt{2x} - 1 \sqrt{2x} - 6 = 0 \\ \\ = > x(x + 3 \sqrt{2} ) - \sqrt{2} (x + 3 \sqrt{2} ) = 0 \\ \\ = > (x + 3 \sqrt{2} )(x - \sqrt{2} ) = 0 \\ \\ = > x + 3 \sqrt{2} = 0 \: \: or \: \: x - \sqrt{2} = 0 \\ \\ = > x = - 3 \sqrt{2} \: \: or \: \: x = \sqrt{2}$

Hope it helps ☺️