You can put this solution on YOUR website! x^2 + 6x + 23 = 0
Rewrie the above as:
x^2 + 6x = -23
To complete the square on the loeft side we need to divide the coefficient on the x term by 2, square it and add the result to both sides:
The coefficient on the x term is 6, so we have (6/2)^2 = 3^2 = 9. Adding 9 to both sides we have:
x^2 + 6x + 9 = -23 + 9
x^2 + 6x + 9 = -14
(x+3)*(x+3) = -14
(x+3)^2 = -14
Taking the square root of both sides:
(x+3)= +sqrt(-14) and
(x+3)= -sqrt(-14)
Note that sqrt(-14) is a complex number, namely i*sqrt(14).
We have then:
x+3 = i*sqrt(14)
x = -3 + i*sqrt914)
and
x+3 = -i*sqrt(14)
x = -3 - i*sqrt(14)
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