Explanation:
[tex] \sqrt{2 {x}^{2} + 8x - 4 } + 6 = 5 \\ 2 {x}^{2} + 8x - 4 + 6 = {5}^{2} \\ ( \sqrt{2x} {)}^{2} + {2}^{2} = 25 \\ {( \sqrt{2} x + 2)}^{2} = 25 \\ ( \sqrt{2} x + 2) = \sqrt{25} \\ ( \sqrt{2} x + 2) = 5 \\ \sqrt{2} x + 2 = 5 \\ \sqrt{2} x = 5 - 2 \\ \sqrt{2} x = 3 \\ 2x = {3}^{2} \\ 2x = 9 \\ x = 9 \div 2 \\ x = 4.5[/tex]