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\begin{aligned} 2 x+3 &=(4)^{2}-2(4) \sqrt{x-2}+(\sqrt{x-2})^{2} & & \\ 2 x+3 &=16-8 \sqrt{x-2}+(x-2) & & \\ 2 x+3 &=14+x-8 \sqrt{x-2} & & \text { Combine like terms. } \\ x-11 &=-8 \sqrt{x-2} & & \text { Isolate the second radical. } \\(x-11)^{2} &=(-8 \sqrt{x-2})^{2} & & \text { Square both sides. } \\ x^{2}-22 x+121 &=64(x-2) & & \end{aligned}