Question

To solve by completing the square, what value should be added to both sides of the equation x^2+4x=-1??????

Answer 1

how would you complete this square?

\begin{array}c
x^2&x&x\\
x&.&.\\
x&.&.\\
\end{array}
in other words, how many places would you have to fill in?

Answer 2

ohhh, i see...sortof. so just four, right? but where would the number go around the box?

Answer 3

the number is just the number of places to make it a complete square; and yes its 4 :)

\begin{array}c
x^2&x&x\\
x&1&2\\
x&3&4\\
\end{array}

the algebra of it is this; we take the (4x) part and split it in 2, so that we can make a frame work to fill in the square.

this gives us a 2x2 are to fill; 2*2 = 4

spose we had x^2 + 6x; we would apply the same concepts;

split the (6x) in half and construct a frame work to fill in; 3x up top and 3x down the side; we have a 3x3 area to fill in so... 3*3 = 9 for that one

Answer 4

nevermind figured it out =D

Answer 5

THANKS THOUGH =D

Answer 6

youre welcome :)

Answer 7

spose we had something a little trickier to work with like

x^2 + 5x; we can still find a number to complete the square, but the picture begins to get too complicated to be useful, but the algebra still applies

take 5 and split it in half: 5/2

now we need to fill in a (5/2)x(5/2) area so: (5/2)*(5/2) = 25/4 as a result