Question

How would you complete the square for 5x^2=2x+1

Answer 1

ok so first of all move the 2x to the left side, so subtract 2x to both sides

Answer 2

Okay, so then I would get 5x^2-2x=1?

Answer 3

Right^

now divide everything by 5

we want the 'x^2' term by itself

Answer 4

And so If I do this then I will get
x^2-2x/5=1/5
right?

Answer 5

Correct

\[\large x^2 - \frac{2}{5}x = \frac{1}{5}\]

So now, we take the coefficient of the 'x' term....and divide it by 2...we then square that result...what do we have from that?

Answer 6

Well if I do this then I get
x^2-1/5=1/5
but wouldn't I also multiply the -1/5 on the other side of the equation so then it would be
x^2-1/5=1/25 because when completing the square whenever you add to one side of an equation you must also add to the other side
then by squaring it I would get
(x^2-1/5)^2=-1/25 and then I would square both sides and get
x-1/5=the square root of negative 1 over 25?
Or did I do something wrong?

Answer 7

Not quite!

you didnt square the result originally

\[\large x^2 - \frac{2}{5}x = \frac{1}{5}\]
Divide 2/5 by 2
\[\large \frac{2}{5} \div 2 = \frac{1}{5}\]
then square the result
\[\large (\frac{1}{5})^2 = \frac{1}{25}\]

and yes THIS you add to both sides of the equation

\[\large x^2 - \frac{2}{5}x + \frac{1}{25} = \frac{1}{5} + \frac{1}{25}\]
\[\large x^2 - \frac{2}{5}x + \frac{1}{25} = \frac{6}{25}\]

Turn the left hand side into a square

\[\large (x - \frac{1}{5})^2 = \frac{6}{25}\]

Can you take it from there?

Answer 8

Yes Thanks for the Help!!:)

Answer 9

Of course :)