Please help me!

Find the exact solutions to the quadratic equation in the complex numbers.
(x-13)²=-36

x = 13 +/- sqrt (-36)

x = 13 +/- 6 i

13 + 6 i
13 - 6 i
note - those are complex conjugates

To find the exact solutions to the quadratic equation (x - 13)² = -36, we can follow these steps:

Step 1: Expand the equation
(x - 13)² = -36
(x - 13)(x - 13) = -36
x² - 26x + 169 = -36

Step 2: Rearrange the equation
x² - 26x + 169 + 36 = 0
x² - 26x + 205 = 0

Step 3: Use the quadratic formula
The quadratic formula is: x = (-b ± √(b² - 4ac)) / 2a

In this equation, a = 1, b = -26, and c = 205.

Substituting these values into the quadratic formula, we get:
x = (-(-26) ± √((-26)² - 4(1)(205))) / (2(1))
x = (26 ± √(676 - 820)) / 2
x = (26 ± √(-144)) / 2

Step 4: Simplify the square root of -144
√(-144) = √(144) * √(-1) = 12i * i = 12i² = 12 * (-1) = -12

Step 5: Solve for x
x = (26 ± √(-144)) / 2
x = (26 ± (-12)) / 2

Step 6: Obtain the two solutions
x₁ = (26 - 12) / 2 = 14 / 2 = 7
x₂ = (26 + 12) / 2 = 38 / 2 = 19

Therefore, the exact solutions to the quadratic equation (x - 13)² = -36 are x = 7 and x = 19.