select the correct answer.\nwhat is the solution to the equation?\n$sqrt{x}+6 = x$\na. 4\nb. 9\nc. 4 and…

Explanation:

Step1: Isolate the square - root term

Subtract 6 from both sides of the equation $\sqrt{x}+6 = x$ to get $\sqrt{x}=x - 6$.

Step2: Square both sides

Squaring both sides gives $(\sqrt{x})^2=(x - 6)^2$. So, $x=x^{2}-12x + 36$.

Step3: Rearrange to a quadratic equation

Rearrange the equation to $x^{2}-13x + 36=0$.

Step4: Factor the quadratic equation

Factor $x^{2}-13x + 36$ as $(x - 4)(x - 9)=0$.

Step5: Solve for x

Set each factor equal to zero: $x-4 = 0$ gives $x = 4$ and $x - 9=0$ gives $x = 9$.

Step6: Check for extraneous solutions

For $x = 4$, $\sqrt{4}+6=2 + 6=8\neq4$. For $x = 9$, $\sqrt{9}+6=3 + 6=9$.

Answer:

B. 9