which equation results from isolating a radical term and squaring both sides of the equation for the…

which equation results from isolating a radical term and squaring both sides of the equation for the equation $sqrt{x + 6}+sqrt{x}=8$?\n$x + 6=64 - x$\n$x + 6=64 + x$\n$x + 6=64 + x-16sqrt{x}$\n$x + 6=64 + x + 16sqrt{x}$

which equation results from isolating a radical term and squaring both sides of the equation for the equation $sqrt{x + 6}+sqrt{x}=8$?\n$x + 6=64 - x$\n$x + 6=64 + x$\n$x + 6=64 + x-16sqrt{x}$\n$x + 6=64 + x + 16sqrt{x}$

Answer

Explanation:

Step1: Isolate a radical term

Isolate $\sqrt{x + 6}$ in the equation $\sqrt{x+6}+\sqrt{x}=8$. We get $\sqrt{x + 6}=8-\sqrt{x}$.

Step2: Square both sides

Square both sides of the equation $\sqrt{x + 6}=8-\sqrt{x}$. Using the formula $(a - b)^2=a^{2}-2ab + b^{2}$, where $a = 8$ and $b=\sqrt{x}$, we have $(\sqrt{x + 6})^2=(8-\sqrt{x})^2$. So $x + 6=64-16\sqrt{x}+x$.

Answer:

C. $x + 6=64+x - 16\sqrt{x}$