Question

how do you solve by completing the sq this problem:
4x^2 + 12x + 19 = 11

Answer 1

first subtract 19, then divide by 4

Answer 2

\[4x^2 + 12x + 19 = 11\]
\[4x^2 + 12x = -8\]
\[x^2+3x=-2\]

Answer 3

then complete the square
\[(x+\frac{3}{2})^2=-2+\frac{9}{4}\]
\[(x+\frac{3}{2})^2=\frac{1}{4}\]

Answer 4

take the square root and get
\[x+\frac{3}{2}=\pm\frac{1}{2}\] then solve the two equation
\[x+\frac{3}{2}=\frac{1}{2}\] and
\[x+\frac{3}{2}=-\frac{1}{2}\] and you are done