Solve: (x-3)^2= -4
x = 3 + 2i
or
x = 3 - 2i
see
http://www.jiskha.com/display.cgi?id=1309805997
To solve the equation (x-3)^2 = -4, we need to isolate the variable x.
Step 1: Expand the equation
(x-3)^2 = (-4)
(x-3)(x-3) = (-4)
(x^2 - 6x + 9) = (-4)
Step 2: Move all terms to one side of the equation
(x^2 - 6x + 9) + 4 = 0
x^2 - 6x + 13 = 0
Step 3: Use the quadratic formula to solve for x
The quadratic formula is given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For the equation x^2 - 6x + 13 = 0, we have:
a = 1, b = -6, c = 13
Substituting these values into the quadratic formula:
x = (-(-6) ± √((-6)^2 - 4(1)(13))) / (2(1))
x = (6 ± √(36 - 52)) / 2
x = (6 ± √(-16)) / 2
Step 4: Simplify the square root expression
Since the expression inside the square root is negative, the equation does not have real solutions. However, it does have complex solutions.
x = (6 ± 4i) / 2
x = 3 ± 2i
Therefore, the solutions to the equation (x-3)^2 = -4 are x = 3 + 2i and x = 3 - 2i.