To solve the equation \( \frac{19 + (x - 3)^2}{-4} = -4 \), we can first eliminate the fraction by multiplying both sides by -4:
\[ 19 + (x - 3)^2 = 16 \]
Next, we subtract 19 from both sides:
\[ (x - 3)^2 = 16 - 19 \] \[ (x - 3)^2 = -3 \]
Now, we notice that \( (x - 3)^2 \) cannot equal -3 because the square of a real number is always non-negative. Thus, this equation does not yield any real solutions.
Since there are no real solutions, let's examine the context of the options provided (A, B, C, and D).
However, none of these options would correctly represent the solution set for this equation.
The final conclusion is that the equation has no real solutions.
1 answer