Chapter 11 - Section 11.1 - Solving Quadratic Equations by Completing the Square - Exercise Set - Page 763: 13

$x=\dfrac{3}{2}\pm\sqrt{2}$

$(2x-3)^{2}=8$ Take the square root of both sides of the equation: $\sqrt{(2x-3)^{2}}=\pm\sqrt{8}$ $2x-3=\pm2\sqrt{2}$ Solve for $x$: $2x=3\pm2\sqrt{2}$ $x=\dfrac{3\pm2\sqrt{2}}{2}$ $x=\dfrac{3}{2}\pm\sqrt{2}$