Solve the equation.
-$\sqrt{x^{2}-9 x+21}=x-5$
A) 46
B) 4
C) $\frac{46}{9}$
D) No solution

Question

Quizplus · Accepted Answer

Squaring both sides of the equation $\sqrt{x^{2}-9 x+21}=x-5$ gives $x^{2}-9x+21=(x-5)^2$. Expanding the right side yields $x^{2}-9x+21=x^2-10x+25$. Simplifying, we get $x=4$. However, substituting $x=4$ back into the original equation, we find that the left side becomes $\sqrt{4^2-9*4+21}=\sqrt{16-36+21}=\sqrt{1}$, which equals 1, while the right side is $4-5=-1$. Since these do not match, the correct answer is that there is no solution.

Solve the Equation x2−9x+21=x−5\sqrt{x^{2}-9 x+21}=x-5x2−9x+21​=x−5 A) 46 B) 4 C) 469\frac{46}{9}946​ D) No Solution

Solve the Equation $\sqrt{x^{2}-9 x+21}=x-5$ A) 46
B) 4
C) $\frac{46}{9}$ D) No Solution