Question

for the trinomial and simplify.
$(x + \boxed{48} \boldsymbol{\times} \
ightarrow -3 )^2 = \boxed{104} \boldsymbol{\times} \
ightarrow 4$
complete
use the square root property of equality to solve
$(x - 3)^2 = -4$
the solutions are
done
-1 or 7
1 or 5
$3 \pm 2i$
$3 \pm 4i$

Explanation:

Step1: Apply square root property

The square root property states that if \(u^2 = v\), then \(u=\pm\sqrt{v}\). For the equation \((x - 3)^2=- 4\), let \(u = x - 3\) and \(v=-4\). So we have \(x - 3=\pm\sqrt{-4}\).

Step2: Simplify the square root of a negative number

Recall that \(\sqrt{-a}=i\sqrt{a}\) for \(a>0\). So \(\sqrt{-4}=i\sqrt{4} = 2i\). Then \(x - 3=\pm2i\).

Step3: Solve for x

Add 3 to both sides of the equation \(x - 3=\pm2i\). We get \(x=3\pm2i\).

Answer:

\(3\pm2i\) (corresponding to the option "3 ± 2i")