[tex] {(x - 3)}^{2} - {(x - 8)}^{2} = (x \sqrt{2} + 1) ^{2} - 2 \times {x}^{2} + 10x \\ \\ {(x - 3)}^{2} - {(x - 8)}^{2} = ( \sqrt{2}x + 1) ^{2} - {2x}^{2} + 10x \\ \\ {x}^{2} - 6x + 9 - {x}^{2} + 16x - 64 = {2x}^{2} + 2 \sqrt{2}x + 1 - {2x}^{2} + 10x \\ \\ 10x - 55 = {2x}^{2} + 2 \sqrt{2}x + 1 - {2x}^{2} + 10x \\ \\ 10x - 55 = 2 \sqrt{2}x + 1 + 10x \\ \\ - 55 = 2 \sqrt{2}x + 1 \\ \\ - 55 - 1 = 2 \sqrt{2}x \\ \\ - 56 = 2 \sqrt{2}x \\ \\ - \frac{56}{2} = \sqrt{2}x \\ \\ - 28 = \sqrt{2}x \\ \\ - \frac{28}{ \sqrt{2} } = x \\ \\ x = - \frac{28}{ \sqrt{2} } [/tex]
