Question

Solve the following quadratic equation using square roots:

−3+(x+12)^2/2=−3
(1 point)
Type the smaller solution first.

Answer 1

To solve the equation

\[
-3 + \frac{(x + 12)^2}{2} = -3,
\]

first, we can eliminate \(-3\) from both sides of the equation:

\[
\frac{(x + 12)^2}{2} = 0.
\]

Next, we can multiply both sides by 2 to get rid of the fraction:

\[
(x + 12)^2 = 0.
\]

Now we take the square root of both sides:

\[
x + 12 = 0.
\]

This implies:

\[
x = -12.
\]

Since this equation has only one solution (a double root), we conclude:

\[
x = -12.
\]

Thus, the answer is

\[
-12.
\]