17. Solve the equation. x-sqrt (16-6x)=0 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is square (Simplify your answer.Use a comma to separate answers as needed.) B. There is no solution.

To solve the equation \( x - \sqrt{16 - 6x} = 0 \), we need to isolate the square root term and then solve for \( x \).<br /><br />First, let's rewrite the equation:<br />\[ x - \sqrt{16 - 6x} = 0 \]<br /><br />Add \(\sqrt{16 - 6x}\) to both sides to isolate the square root term:<br />\[ x = \sqrt{16 - 6x} \]<br /><br />Next, square both sides to eliminate the square root:<br />\[ x^2 = 16 - 6x \]<br /><br />Rearrange the equation to standard quadratic form:<br />\[ x^2 + 6x - 16 = 0 \]<br /><br />Now, we can solve this quadratic equation using the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \), where \( a = 1 \), \( b = 6 \), and \( c = -16 \).<br /><br />Calculate the discriminant:<br />\[ \Delta = b^2 - 4ac = 6^2 - 4(1)(-16) = 36 + 64 = 100 \]<br /><br />Now, apply the quadratic formula:<br />\[ x = \frac{-6 \pm \sqrt{100}}{2 \cdot 1} \]<br />\[ x = \frac{-6 \pm 10}{2} \]<br /><br />This gives us two solutions:<br />\[ x = \frac{-6 + 10}{2} = \frac{4}{2} = 2 \]<br />\[ x = \frac{-6 - 10}{2} = \frac{-16}{2} = -8 \]<br /><br />We need to check these solutions in the original equation to ensure they are valid.<br /><br />For \( x = 2 \):<br />\[ 2 - \sqrt{16 - 6 \cdot 2} = 2 - \sqrt{16 - 12} = 2 - \sqrt{4} = 2 - 2 = 0 \]<br />This is a valid solution.<br /><br />For \( x = -8 \):<br />\[ -8 - \sqrt{16 - 6 \cdot (-8)} = -8 - \sqrt{16 + 48} = -8 - \sqrt{64} = -8 - 8 = -16 \]<br />This does not satisfy the original equation.<br /><br />Therefore, the only valid solution is \( x = 2 \).<br /><br />So, the correct choice is:<br />A. The solution set is \( \{2\} \)