5. Solve the equation. Show your work. (Note: This is already solved for you; you are just typing this out like you see it to practice showing work for a multistep problem.) \( x ^ { 2 } - 4 x + 13 = 0 \) 

1. Subtract \( 13 \) from both sides. \( x ^ { 2 } - 4 x = - 13 \) 

2. Divide the \( 4 \) in half and square it to complete the square. Add this number to both sides. \( x ^ { 2 } - 4 x + 4 = - 13 + 4 \) 

3. Factor the perfect square and simplify the right side. \( ( x - 2 ) ^ { 2 } = - 9 \) 

4. Take the square root of both sides to eliminate the exponent. \( x - 2 = \pm \sqrt { - 9 } \) 

5. Simplify the radical and isolate the \( x . x = 2 \pm 3 i\)