+983 \(\sqrt{2x-5}+4=x\\ \sqrt{2x-5}+4-4=x-4\\ \sqrt{2x-5}=x-4\\ (\sqrt{2x-5})^2=(x-4)^2\\ 2x-5=x^2-8x+16\\ x^2-10x+21=0\\ (x-7)(x-3)=0\\ x_1=7, x_2 = 3 \)
We plug the solutions to verify:
\(\sqrt{2\cdot7-5}+4=7\\ \sqrt9+4=7\\ 3+4=7\\\)
Seven works!
\(\sqrt{2\cdot3-5}+4=3\\ \sqrt1+4=3\\ 5\ne3\\\)
Three doesn’t work.
Therefore, the answer you seek is 7!
I hope this helped,
Gavin
+983 \(\sqrt{2x-5}+4=x\\ \sqrt{2x-5}+4-4=x-4\\ \sqrt{2x-5}=x-4\\ (\sqrt{2x-5})^2=(x-4)^2\\ 2x-5=x^2-8x+16\\ x^2-10x+21=0\\ (x-7)(x-3)=0\\ x_1=7, x_2 = 3 \)
We plug the solutions to verify:
\(\sqrt{2\cdot7-5}+4=7\\ \sqrt9+4=7\\ 3+4=7\\\)
Seven works!
\(\sqrt{2\cdot3-5}+4=3\\ \sqrt1+4=3\\ 5\ne3\\\)
Three doesn’t work.
Therefore, the answer you seek is 7!
I hope this helped,
Gavin
