4a^2 + 4b^2 + 33a + 33b =-8 solve for a in terms on b by factoring.

Answer 1

Hi Kyla

4a^2 + 4b^2 + 33a + 33b =-8 solve for a in terms on b by factoring.

If you meant solve a in terms of b by factoring then we can start be regrouping

4a² - 33a + 4b² + 33b = -8

Next we could move the b terms over to one side of the equation and the a terms and constant to the other

4a² - 33a + 8 = -4b² - 33b

We can also factor both sides

(4a - 1)(a - 8) = -b(4b + 33)

In terms of b, when b = 0 then

(4a - 1) = 0

a = 1/4

(a - 8) = 0

a = 8

Answer 2

4a^2 + 33a + 4b^2 + 33b = -8

4( a^2 + (33/4)a ) + 4(b^2 + (33/4)b ) = -8

completing of the square: [(33/4)*(1/2)]^2 = (33/8)^2 = 1089/64

4(a^2 + (33/4)a + 1089/64) + 4( b^2 + (33/4)b +1089/64) = -8+ 1089/16 + 1089/16

4( a + 33/8)^2 + 4(b + 33/8)^2 = (-128+1089+1089)/16

4( a + 33/8)^2 + 4(b + 33/8)^2 = 2050/16

(a+33/8)^2+(b+33/8)^2 = 1025/32

(a+33/8)^2 = (1025/32) - (b+ 33/8)^2

a+33/8 = +or- sqrt( (1025/32) - (b + 33/8)^2 )