How do you find the roots, real and imaginary, of #y= x^2 - 8x + (x+4)^2 # using the quadratic formula?

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Answer 1 · 2018-05-12T02:58:55

#color(maroon)("two roots are " +2sqrt2 i, -2sqrt2 i#

#y = x^2 - 8x + (x + 4)^2#

#y = x^2 - 8x + x^2 + 8x + 16#

#y = 2x^2 + 16#

#x = (-b +- sqrt(b^2 - 4ac)) / (2a)#

#a = 2, b = 0, c = 16#

#x = (0 +- sqrt(0 - 128)) / 4#

#x = +- 8sqrt(-2) / 4 = +- 2 sqrt(-2)#

#color(maroon)(x = + 2sqrt2 i, -2sqrt2 i#