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

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

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

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

$y = 2x^2 + 16$

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

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

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

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

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

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