How many solutions How many solutions are in the solution set for the following equation? -3(x-5)^2=12 Zero 2 1 4

To find the number of solutions for the equation $-3(x-5)^{2}=12$, we need to solve the equation.<br /><br />Step 1: Divide both sides of the equation by -3 to isolate the squared term.<br />$(x-5)^{2} = -4$<br /><br />Step 2: Take the square root of both sides of the equation.<br />$x-5 = \pm \sqrt{-4}$<br /><br />Step 3: Simplify the square root.<br />$x-5 = \pm 2i$<br /><br />Step 4: Solve for x by adding 5 to both sides of the equation.<br />$x = 5 \pm 2i$<br /><br />The solutions are $x = 5 + 2i$ and $x = 5 - 2i$. Therefore, there are 2 solutions in the solution set for the given equation.<br /><br />Answer: 2