Someone please give me an example of how to do this Alg problem?

Question

I need to complete the square of a quadratic equation and then reduce to one of these standard forms Y-b = A(x-a)^2 or x-a = A(y-b)^2.

Can someone please show me with this problem:

3x^2 + 3x + 2y = 0

Answer 1

3x² + 3x + 2y = 0  

First move all the x terms to the right side of the equation, and divide through by the coefficient of the y term on the left side.  Then factor out any common factors found in the coefficients of the x terms:

2y = -3x² - 3x

y = -3/2 x² - 3/2 x

y = -3/2 (x² + x)

Here is the general plan of attack.  We will complete the trinomial square on the right side by dividing the coefficient of the linear x term by 2.  Then we will square that result and add it to both sides of the equation.  Remember that there is a constant in front of the expression on the right side, so the number added to complete the trinomial must be multiplied by that constant when added to the left side.  

The coefficient of the linear x term is +1.  So the number to be added on the right side is +(1/2)² = ¼.  That number is multiplied by the constant -3/2 before the quadratic expression on the right side, so what we are actually doing is subtracting (3/2)(¼) = 3/8 from that side.  To keep the equation balanced, we must also subtract 3/8 from the left side.  We show that below:

y = -3/2 (x² + x)

y + (-3/2)(½)² = -3/2 [x² + x + (½)²]

y + (-3/2)(¼) = -3/2 (x² + x + ¼)

y - 3/8 = -3/2 (x² + x + ¼).

Now we have our revised equation with the completed trinomial square on the right side as shown on the last line above.

All that remains to be done to our equation is to write the variable expression as a binomial squared.  x² + x + ¼ = (x + ½)², so we rewrite the expression in that form to get this:

y - 3/8 = -3/2 (x + ½)².

We now have the equation in this standard form:

y - b = A (x - a)², where A = -3/2, a = -½, and b = 3/8.

Now we need to verify that our result works.  Using the original equation and letting x = 1, we get this:

y = -3/2 (x² + x)

y = -3/2 [(1)² + 1]

y = -3/2 (2)

y = -3

Let's see if we get the same result using the new equattion.

y - 3/8 = -3/2 (x + ½)² ----> y = -3/2 (x + ½)² + 3/8.

Let x = 1 again:

y = -3/2 (1 + ½)² + 3/8

y = -3/2 (3/2)² + 3/8

y = -3/2 (9/4) + 3/8

y = -27/8 + 3/8

y = (-27 + 3)/8

y = -24/8

y = -3

If we plug other values for x into the new equation, we will find that they also produce equivalent results, so we have the correct equation:

y - 3/8 = -3/2 (x + ½)².

Answer 2

3x^2 + 3x + 2y = 0 group similar terms

( 3x^2 + 3x ) + 2y = 0  take out three

3 ( x^2 + x ) + 2y = 0  complete the square

3( x^2 +x + 1/4) + 2y = 0 + 1/4  simplify

3(x + 1/2)^2 +2y = 1/4 simplify further to your desired form

2y - 1/4 = - 3(x + 1/2)^2

Answer 3

if u r in college ... den i cud b ur collegemate.. coz i hav got to do the same quesn