Quadratic Equation

**Mist** · October 14th 2009, 05:25 AM

I'm finding it difficult to solve this question
It's solving quadratic eqaution by completing the square

x^2+6x+1=0

Any help?

**craig** · October 14th 2009, 05:33 AM

Originally Posted by Mist

I'm finding it difficult to solve this question
It's solving quadratic eqaution by completing the square

x^2+6x+1=0

Any help?

Here's how I'd proceed.

When solving the square of a quadratic in the form $x^2 + 2bx +c = 0$ , first you put into brackets, $(x+b)^2 + c = 0$ .

So in the case of your question you get $(x+3)^2 +1 = 0$ . However, if you multiply out $(x+3)^2$ ,you find that you get an extra 9 in your equation, to compensate for this you also place a -9 in your equation, giving you $(x+3)^2 - 9 +1 = 0$ .

A little bit of rearranging should give you $(x+3)^2 = 8$ , which in turn leads to $x+3 = \pm2\sqrt{2}$ .

I presume you can continue from here to find the two solutions.

Craig

**masters** · October 14th 2009, 05:34 AM

Originally Posted by Mist

I'm finding it difficult to solve this question
It's solving quadratic eqaution by completing the square

x^2+6x+1=0

Any help?

Hi Mist,

Step 1: Transpose the constant to the right hand side.

$x^2+6x=-1$

Step 2: Take half the coefficent of the linear term (x), square it, and add the result to both sides of the equation.

$x^2+6x+9=-1+9$

Step 3: You have just made the left side a perfect square trinomial.

$(x+3)^2=8$

Step 4: Take the square root of both sides.

$x+3=\pm \sqrt{8}$

I'll bet you can finish up, can't you?

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