To solve the equation [tex]\( -2 \sqrt{x} + 4 = -12 \)[/tex], follow these steps:
1. Start by isolating the term with the square root on one side. Subtract 4 from both sides of the equation:
[tex]\[
-2 \sqrt{x} + 4 - 4 = -12 - 4
\][/tex]
Simplifying this, we get:
[tex]\[
-2 \sqrt{x} = -16
\][/tex]
2. Next, divide both sides of the equation by -2 to isolate the square root term:
[tex]\[
\frac{-2 \sqrt{x}}{-2} = \frac{-16}{-2}
\][/tex]
Simplifying this, we get:
[tex]\[
\sqrt{x} = 8
\][/tex]
3. Now, square both sides to eliminate the square root:
[tex]\[
(\sqrt{x})^2 = 8^2
\][/tex]
Simplifying this, we get:
[tex]\[
x = 64
\][/tex]
Therefore, the solution to the equation [tex]\( -2 \sqrt{x} + 4 = -12 \)[/tex] is [tex]\( x = 64 \)[/tex].
The correct answer is:
D. 64
