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

Question

Quizplus · Accepted Answer

To solve the equation $\sqrt{x + 7} + 5 = x$, first isolate the square root by subtracting 5 from both sides: $\sqrt{x + 7} = x - 5$. Then square both sides to eliminate the square root: $x + 7 = (x - 5)^2$. Expanding the right side gives $x + 7 = x^2 - 10x + 25$. Rearranging to form a quadratic equation: $x^2 - 11x + 18 = 0$. Factoring this equation gives $(x - 9)(x - 2) = 0$, 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 $\sqrt{9 + 7} + 5 = 9$, 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 is $x = 9$.

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

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