Question

Solve the equation for x. If a solution is extraneous, be sure to identify it in your final answer.

SHOW STEP BY STEP

Answer 1

Answer: x = 7

Explanation:

`√(x-3)+5=x\quad \rightarrow\quad Domain: x\geq5\\\\√(x-3)=x-5\qquad added\ 5\ to\ both\ sides\\\\(√(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}`