Question

Solve the equation by completing the square.
2x^2 + 4x + 1 = 0

Answer 1

ax^2+bx+c=0
The coefficient of x^2 must be 1, so factor 'a' out

a(x^2+bx/a)+c=0
divide bx/a by 2,then set the x^2 becomes x only,eliminate the x from b/a, then square the whole bracket

you ended up with

a(x+b/2a)^2+c=0

then, you need to bring the b/2a OUT the brackets and square it, and when you bring it out, it is always negative, be sure that the 'a' will be multiplying the one you bought it out

a(x+b/2a)^2-(b/2a)^2(a)+c=0

Answer 2

first step
2*(x+1)^2-1 = 0

Answer 3

2x^2 + 4x + 1 = 0
2(x^2+2x)+1=0
2(x+1)^2-1(2)+1=0
2(x+1)^2-1=0
(x+1)^2=1/2
square root both sides and then minus 1 from both sides and you're done

Answer 4

\[2x^2 + 4x + 1 = 0 \implies x^2 + 2x = -1/2\implies x^2 + 2x +1= 1-1/2\]\[\implies (x+1)^2=1/2\implies x+1=\pm \frac{\sqrt2}{2} \implies x=-1\pm \frac{\sqrt2}{2}\]

Answer 5

Thank you! That one has had me confused!

Answer 6

http://www.khanacademy.org/math/algebra/quadtratics/v/completing-the-square

video!

Answer 7

Wow thanks!