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

Question

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

Quizplus · Accepted Answer

To solve the equation $\sqrt{x + 7} + 5 = x$, first isolate the square root term: $\sqrt{x + 7} = x - 5$. Then square both sides to eliminate the square root: $(x - 5)^2 = x + 7$. Expanding the left side gives $x^2 - 10x + 25 = x + 7$. Rearranging terms yields $x^2 - 11x + 18 = 0$. Factoring the quadratic equation gives $(x - 9)(x - 2) = 0$, which has solutions $x = 9$ and $x = 2$. 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 $\sqrt{9 + 7} + 5 = 9$, which simplifies to $4 + 5 = 9$, a true statement. Substituting $x = 2$ gives $\sqrt{2 + 7} + 5 = 2$, which simplifies to $3 + 5 = 2$, a false statement. Therefore, the only solution that satisfies the original equation is $x = 9$.

Solve the Equation - x+7+5=x\sqrt { x + 7 } + 5 = xx+7​+5=x

Solve the Equation
- $\sqrt { x + 7 } + 5 = x$