Answer: x = 7
Step-by-step explanation:
[tex]\sqrt{x-3}+5=x\quad \rightarrow\quad Domain: x\geq5\\\\\sqrt{x-3}=x-5\qquad added\ 5\ to\ both\ sides\\\\(\sqrt{x-3})^2=(x-5)^2\qquad squared\ both\ sides\\\\x-3=x^2-10x+25\qquad simplified\\\\0=x^2-11x+28\qquad subtracted\ x-3\ from\ both\ sides\\\\0=(x-7)(x-4)\qquad factored\ right\ side\\\\0=x-7\quad 0=x-4\qquad applied\ Zero\ Product\ Property\\\\x=7\qquad x=4\qquad \qquad solved\ for\ x\\\\\text{Since }x\geq5, \text{x = 4 is an extraneous (not valid) solution}\\So, \large\boxed{x=7}[/tex]
