Question

how do you solve 4x squared+16x+12=0 by completing the square?

Answer 1

to complete the squre you want to have the lead coefficient equal to +1; when you have an equation you can just divide by the lead coefficient, 4 in this case\[x^2+4x+3=0\]are you aware that this factors and one does not usually complete the square on a factorable equation... but i will continue

Answer 2

if the equation does not factor, you want to produce a constant that makes it factorable as a perfect square trinomial (complete the square); so subtract the 3 onto the RHS of the equation\[x^2+4x=0\]

Answer 3

now take half of the middle coefficient, square it, and add it to both sides of the equation; in this case (4/2)^2=2^2=4\[x^2+4x+4=-3+4\]no wfactor the LHS as a perfect square trinomial\[(x+2)^2=1\]

Answer 4

to finish take the square root of both sides and subtract 2 to solve for x\[x+2=\pm \sqrt{1}\]\[x=-2 \pm 1\]\[x=-3 \cup x=-1\]

Answer 5

the reason we don't usually complete the square on equations that factor is consider this solution\[x^2+4x+3=0\]\[(x+3)(x+1)=0\]\[x=-3 \cup x=-1\]

Answer 6

much easier!

Answer 7

thanks!

Answer 8

ur welcome