X^2+8x+28=0 using completing the square method

Get the constant on one side

x^2 + 8x = -28

divide the coefficient (8) by 2 and square it. then add that number to both sides.

x^2 + 8x + 16 = -12

factor

(x + 4)(x + 4) = -12

square root both sides

x + 4 = sqrt(-12)

subtract 4 to both sides

x = sqrt(-12) - 4

we cannot calculate the square root of negative numbers without imaginary numbers, so unless you are expected to use imaginary numbers you can stop here and say "no solution" but include the equation to show you worked the problem out to the fullest extent.

quadratic equations usually have 2 answers because square roots are ambiguous, so if you continued you would get two answers.

however since a negative times a negative is a positive number, negative roots do not have a real number answer.