# Another square technique...

• May 20th 2010, 07:01 AM
Another square technique...
Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

2x2 + 32x + 12 = 0

Thanks alot guys.
• May 20th 2010, 07:16 AM
harish21
Quote:

Use the technique of completing the square to transform the quadratic equation into the form (x + c)2 = a.

2x2 + 32x + 12 = 0

Thanks alot guys.

$\displaystyle 2x^{2} + 32x + 12 = 0$

$\displaystyle 2(x^{2} + 16x + 6 = 0)$

$\displaystyle x^{2} + 16x + 6 = 0$

$\displaystyle x^2 + 2\times 8\times x + 6 = 0$

Can you take it further? Please try
• May 20th 2010, 07:26 AM
Quote:

Originally Posted by harish21
$\displaystyle 2x^{2} + 32x + 12 = 0$

$\displaystyle 2(x^{2} + 16x + 6 = 0)$

$\displaystyle x^{2} + 16x + 6 = 0$

$\displaystyle x^2 + 2\times 8\times x + 6 = 0$

Can you take it further? Please try

Would it be (x + 6)2 = 58 ?
• May 20th 2010, 07:43 AM
harish21
Quote:

Would it be (x + 6)2 = 58 ?

No.

You are left with $\displaystyle x^2+ 2\times x \times 8 + 6 = 0$.....(I)

So $\displaystyle (x+c)^2 = x^2+ 2.x.c +c^2$...(II)

if you compare I and II, you should see that c = 8.

So you need to have $\displaystyle (x+8)^2$, which is equal to $\displaystyle x^2 + 2.x.8+ 64$

now if you look at equation (I) again, you already have $\displaystyle x^2+ 2\times x \times 8 + 6 = 0$.

To make this $\displaystyle x^2+ 2\times x \times 8 + 64 = 0$,

you need to add 58 right?

so,

$\displaystyle x^2+ 2\times x \times 8 + 6 +58 -58= 0$

Now put the above equation in the form of $\displaystyle (x+c)^2=a$
• May 20th 2010, 07:55 AM
Quote:

Originally Posted by harish21
No.

You are left with $\displaystyle x^2+ 2\times x \times 8 + 6 = 0$.....(I)

So $\displaystyle (x+c)^2 = x^2+ 2.x.c +c^2$...(II)

if you compare I and II, you should see that c = 8.

So you need to have $\displaystyle (x+8)^2$, which is equal to $\displaystyle x^2 + 2.x.8+ 64$

now if you look at equation (I) again, you already have $\displaystyle x^2+ 2\times x \times 8 + 6 = 0$.

To make this $\displaystyle x^2+ 2\times x \times 8 + 64 = 0$,

you need to add 58 right?

so,

$\displaystyle x^2+ 2\times x \times 8 + 6 +58 -58= 0$

Now put the above equation in the form of $\displaystyle (x+c)^2=a$

$\displaystyle (x + 8)2 = 58$ would be it than right?
• May 20th 2010, 08:08 AM
harish21
Quote:

$\displaystyle (x + 8)2 = 58$ would be it than right?