Complete the square 4y^2+3x^2=3-x
First, let's rewrite the equation in standard form:
4y^2 + 3x^2 + x - 3 = 0
To complete the square for the y terms, factor out the 4 in front of y^2:
4(y^2 + (3/4)y) + 3x^2 + x - 3 = 0
Next, complete the square for the y terms by adding and subtracting (3/8)^2 = 9/64:
4(y^2 + (3/4)y + 9/64 - 9/64) + 3x^2 + x - 3 = 0
Now, rewrite the y terms as a perfect square trinomial:
4(y + 3/8)^2 - 9/4 + 3x^2 + x - 3 = 0
Rearranging the terms:
4(y + 3/8)^2 + 3x^2 + x - 3- 9/4= 0
Multiplying throughout by 4:
16(y + 3/8)^2 + 12x^2 + 4x - 12 - 9 = 0
Now the equation is in the form of a completed square.