solve the equation $-(x - 3)^2 - 3 = 7$ and re-express the answer as a complex number in the standard form $a pm bi$. (1 point)

Question

Accepted Answer

# Explanation:
## Step1: Isolate the squared term
Start with the equation $-(x - 3)^2 - 3 = 7$. First, add 3 to both sides to isolate the squared term.
$$
\begin{align*}
-(x - 3)^2 - 3 + 3&= 7 + 3\
-(x - 3)^2&= 10
\end{align*}
$$
## Step2: Solve for $(x - 3)^2$
Multiply both sides by -1 to solve for $(x - 3)^2$.
$$
\begin{align*}
(-1)\times-(x - 3)^2&= 10\times(-1)\
(x - 3)^2&= -10
\end{align*}
$$
## Step3: Take square roots
Take the square root of both sides. Remember that $\sqrt{-10}=\sqrt{10}\times\sqrt{-1}=i\sqrt{10}$.
$$
\begin{align*}
x - 3&=\pm\sqrt{-10}\
x - 3&=\pm i\sqrt{10}
\end{align*}
$$
## Step4: Solve for $x$
Add 3 to both sides to solve for $x$.
$$
\begin{align*}
x&= 3\pm i\sqrt{10}
\end{align*}
$$
# Answer:
$3 \pm i\sqrt{10}$

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QUESTION IMAGE

Question

Explanation:

Step1: Isolate the squared term

Step2: Solve for \((x - 3)^2\)

Step3: Take square roots

Step4: Solve for \(x\)

Answer: