Chapter 10 - Radical Expressions and Equations - 10-4 Solving Radical Equations - Practice and Problem-Solving Exercises - Page 624: 29

$x=-7$ is extraneous

$Given,$ $x=\sqrt (28-3x)$ Checking for $x=-7$: $L.H.S=-7$ $R.H.S=\sqrt (28-3X(-7))=\sqrt (28+21)=\sqrt 49=7$ $L.H.S$ does not equal $R.H.S$,hence extraneous Checking for $x=4$: $L.H.S=4$ $R.H.S=\sqrt (28-3X4)=\sqrt (28-12)=\sqrt 16=4$ $L.H.S=R.H.S$,hence not extraneous