Question

How do you get:
http://upload.wikimedia.org/math/6/a/e/6ae9933caa1cd431d0e7d8486a564faf.png

to http://upload.wikimedia.org/math/d/6/6/d66c3484dff42c36e8f2da794b07b14e.png ?? (Quadratic equations, completing the square)

Answer 1

hi,
\[x^{2} + 6x + 5 = 0 \]
now consider the expand form of perfect square (x + 3)^2..
\[(x + 3)^{2} = x^{2} + 6x + 9\]
if u subtract 4 from the above expansion...\[x^{2} + 6x + 9 - 4 = x^{2} + 6x + 5\]
u wil c that u can get the original quadratic expression
so ucan write...
\[(x + 3)^{2} -4 = x^{2} + 6x + 9 - 4 = x^{2} + 6x + 5\]
that's the concept for the problem ....

Answer 2

how about this example

"
We illustrate use of this algorithm by solving 2x^2+4x-4=0
x^2+2x-2=0
x^2+2x=2
x^2+2x+1=2+1
\left(x+1 \right)^2=3
x+1=\pm\sqrt{3}
x=-1\pm\sqrt{3}"

Answer 3

Here.. is the technique...
consider the expression..
x^2 + 6x + 5 = 0
to make it a complete square...
first..
co efficient of x should be 1
here we don't have to do anything about it 'cause the coefficient of "x^2" is 1
but if u got an expression with 3x^2 or something then u have to divide the whole problem by 3 and turn the coefficient to 1

second step..
write a perfect square using the following steps..

now u have to subtract the additional amount...
in ur case...

then u can have the final answer...

hope this will help ya!!!