How do you solve by completing the square for $x^{2} + 2 x + 6 = 0$ $x^2+2x+6=0$ ?

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Answer 1 · 2015-05-16T17:38:27

y = x^2 + 2x + 6.

This quadratic equation doesn't have real roots. It has 2 complex roots.

Answer 2 · 2015-05-17T11:51:28

$0 = x^{2} + 2 x + 6 = x^{2} + 2 x + 1 + 5 = {(x + 1)}^{2} + 5$ $0 = x^2+2x+6 = x^2+2x+1+5 = (x+1)^2+5$

Subtracting 5 from both sides we get

${(x + 1)}^{2} = - 5$ $(x+1)^2 = -5$

The square of any real number is positive or zero, so this has no solutions for real values of $x$ $x$ .

How do you solve by completing the square for x2+2x+6=0x^2+2x+6=0?