Question

Solve the quadratic equation by completing the square.

x^2 + 6x - 5 = 0

Answer 1

\[x^2+6x=5\]
\[(x+3)^2=5+3^2=5+9=14\]
\[x+3=\pm\sqrt{14}\]
\[x=-3\pm\sqrt{14}\]

Answer 2

much much easier than the stupid quadratic formula, because the middle term \(6x\) has and even coefficient,
half of 6 is 3, and 3 squared is 9, so nice and neat in this case

Answer 3

x^2 + 6x -5=0
half the coefficient of x
put into completing the square format and always subtract the constant inside the bracket squared
and you get
(x+3)^2 - 9 - 5 = 0
(x+3)^2 - 14=0
add 14 to both sides
(x+3)^2=14
square root both sides
x+3= +/-root 14
subtract three
x=-3+/-root14