Question

Determine the number that will complete the square to solve the equation after the constant has been written on the right-hand side.

Answer 1

\[x^{2} -14x-15=0\]

Answer 2

Remember that if you had the following square: \[
(a+b)^2
\]And expand it you get: \[
(a+b)^2 = a^2 + 2ab + b^2
\]So to complete the square, you need to identify \(a\) and \(b\).
Then you need to pull out \(b\).

Answer 3

We start by identifying \(a=x\).

Answer 4

This means: \(2xb = -14x\). So you solve for \(b\). Can you do it? @cralls18

Answer 5

Basically \[
(a+b)^2 = a^2 + 2ab + b^2 \\
\]With \[
x^2 - 14x-15
\]We have \(a = x\). This means that: \[
2ab = -14x \implies 2xb = -14x
\]

Answer 6

@cralls18
Can you solve for \(b\) here?

Answer 7

do u subtract 2x? from both sides.

Answer 8

Yes!

Answer 9

so -16x?

Answer 10

Whoops... I misread. You don't subtract, you divide both sides by \(2x\).

Answer 11

-7?

Answer 12

Yes. So our square is \[
(x+(-7))^2
\]Can you expand it using FOIL?

Answer 13

ok.. x(sqrd)-14x+49

Answer 14

Yes.
\[
(x-7)^2 = s^2-14x+49
\]But the problem is that this isn't equal to: \[
x^2 -14x -15
\]

Answer 15

not \(s\) meand \(x\) up there.

Answer 16

A. -4

B. 10

C. 49

D. None of these.

E. 4
those are my answers.....

Answer 17

We want to find: \[
(x-7)^2 +c = x^2 -14x-15
\]Expanding this gets: \[
x^2 - 14x + 49 + c = x^2 -14x-15
\]Can you solve for \(c\)?

Answer 18

Actually, maybe we've done enough.

Answer 19

Just take the coefficient of x (-14) divide it by 2, and then square that number...

(-14/2)^2

Answer 20

It looks like they're asking for 49.

Answer 21

ok. thx