Question

factor the trinomial and simplify:
\\((x + -3)^2 = -4\\)

complete

use the square root property of equality to solve \\((x - 3)^2 = -4\\).

the solutions are dropdown
-1 or 7
1 or 5
3 \pm 2i
3 \pm 4i

Explanation:

⚡ Using what you learned: Introduction to Complex Numbers

Step 1: Apply the square root property

Take the square root of both sides of the equation:

$$ (x - 3)^2 = -4 $$

$$ x - 3 = \pm\sqrt{-4} $$

Step 2: Simplify the imaginary number

Using the definition of the imaginary unit \( i = \sqrt{-1} \):

$$ \sqrt{-4} = \sqrt{4} \cdot \sqrt{-1} = 2i $$

$$ x - 3 = \pm 2i $$

Step 3: Solve for x

Add \( 3 \) to both sides to isolate \( x \):

$$ x = 3 \pm 2i $$

Answer:

\( 3 \pm 2i \)