Solve the equation.
-$\sqrt{\mathrm{x}+7}+5=\mathrm{x}$
A) $\{2,9\}$
B) $\{9,18\}$
C) $\{9\}$
D) $\{2\}$

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt{x+7}+5=x$, we first isolate the square root by subtracting 5 from both sides, giving $\sqrt{x+7}=x-5$. Squaring both sides to eliminate the square root gives $x+7=(x-5)^2$. Expanding and simplifying, we get $x+7=x^2-10x+25$, which simplifies to $x^2-11x+18=0$. Factoring, we find $(x-9)(x-2)=0$, so $x=9$ or $x=2$. However, we must check these solutions in the original equation because squaring both sides can introduce extraneous solutions. Substituting $x=9$ into the original equation gives a true statement, while $x=2$ does not satisfy the original equation. Therefore, the only solution is $x=9$.

Solve the Equation x+7+5=x\sqrt{\mathrm{x}+7}+5=\mathrm{x}x+7​+5=x A) {2,9}\{2,9\}{2,9} B) {9,18}\{9,18\}{9,18} C) {9}\{9\}{9} D) {2}\{2\}{2}

Solve the Equation $\sqrt{\mathrm{x}+7}+5=\mathrm{x}$ A) $\{2,9\}$ B) $\{9,18\}$ C) $\{9\}$ D) $\{2\}$