Question

What term is needed to add to each side to complete the square?

x^2+4x=5

Answer 1

you subtract 4 from each side. because you can factor the expression
\[x^2 +4x +4 \]

Answer 2

into (x+2)^2

Answer 3

how about 2x^2+4x=8

Answer 4

@whpalmer4

Answer 5

Well, you can factor out a 2 from everything, so you should do so.

Answer 6

whoops im so sorry, I said subtract, but I meant add 4.

Answer 7

i dont understand

Answer 8

\[2x^2+4x=8\]Divide everything by 2
\[x^2+2x=4\]
now complete the square

Answer 9

how? subtract 4?

Answer 10

Take half of the coefficient of \(x\). Square it. Add to both sides. Rewrite the left side as a perfect square \((x+a)^2\) where \(a\) is half of the coefficient of \(x\).

Answer 11

so 6? how would i write it/

Answer 12

what is 6?

Answer 13

half of the coefficient is 1^ so 4+1=5

Answer 14

okay, 5 isn't 6, but go on, 5 is better here :-)

Answer 15

so the tern is 2 idk how to write it it just asks for the term

Answer 16

is it (x+2)^2?

Answer 17

Okay, here's how you check your work: multiply it out. Does it give you the right answer? If not, it's probably wrong.

You haven't told me what your equation looks like after completing the square, so I can't do it for you.

Answer 18

x^+2x=5

Answer 19

Try typing that again.

Answer 20

x^+2x-5?

Answer 21

I have to go, so I'll just show you.

\[x^2 + 2x = 4\]The coefficient of \(x = 2\), so \(a = 2/2 = 1\)
We have to add \(a^2\) to both sides:

\[x^2+2x+1 = 4+1\]\[x^2+2x+1 = 5\]Now you can rewrite the left side as \((x+a)^2\)
\[(x+1)^2 = 5\]

Check the work:
\[(x+1)(x+1) = 5\]\[x^2 + 1x+1x + 1 = 5\]\[x^2 + 2x + 1 = 5\]\[x^2+2x +1-1 = 5-1\]\[x^2 + 2x = 4\]
That matches our original equation after we factored out a \(2\) from all the terms, so it is correct.

Answer 22

\[2(x^2+2x = 4)\]\[2x^2 + 4x = 8\]