Question

What number would you add to the equation below to complete the square? x2 + 18x = 0

Answer 1

do you know what a "perfect square trinomial" is?

Answer 2

no

Answer 3

\(\bf \large {\color{blue}{ a}}^2\pm2ab+{\color{blue}{ b}}^2\implies ({\color{blue}{ a}}\pm {\color{blue}{ b}})^2\)
^
perfect square trinomial

notice the expanded version, specially the MIDDLE term
the middle term is 2 * the other 2 guys

Answer 4

so keeping in mind the MIDDLE term, let us group the expression first
\(\large{ \bf x^2 + 18x = 0\implies (x^2 + 18x) = 0\\ \quad \\
\implies (x^2 + 18x+{\color{red}{ \square }}^2) = 0}\)

so... what do you think we can use there?

Answer 5

would it be half of 18?

Answer 6

so 9

Answer 7

?

Answer 8

hmm yes
keep in mind that all we're doing is BORROWING FROM ZERO, 0,
so if we ADD \(9^2\) we also have to SUBTRACT \(9^2\)
thus \(\bf x^2 + 18x = 0\implies (x^2 + 18x) = 0\\ \quad \\
\implies (x^2 + 18x+{\color{red}{ 9 }}^2) -{\color{red}{ 9 }}^2= 0\implies (x+9)^2-9=0\implies (x+9)^2=9\)

Answer 9

woops, got a bit truncated... ok so \(\bf x^2 + 18x = 0\implies (x^2 + 18x) = 0\\ \quad \\
\implies (x^2 + 18x+{\color{red}{ 9 }}^2) -{\color{red}{ 9 }}^2= 0\\ \quad \\\implies (x+9)^2-9=0\implies (x+9)^2=9\)

Answer 10

so (x+9)^2=9

Answer 11

so (x+9)^2=9 \(\large \checkmark\)

Answer 12

is our finale answer

Answer 13

yeap

Answer 14

welp its not one of my answer choices

(x+3)^2=9

(x+9)^2=81
(x+18)^2=81
or this fraction one which i dont believe is right

Answer 15

(x+3)^2=9 <---

(x+9)^2=81
(x+18)^2=81

Answer 16

ohh smokes... that's different..hmm

Answer 17

ohh shoot... dohhh, I missed something my bad

Answer 18

\(\bf x^2 + 18x = 0\implies (x^2 + 18x) = 0\\ \quad \\
\implies (x^2 + 18x+{\color{red}{ 9 }}^2) -{\color{red}{ 9 }}^{\huge 2}= 0\)

Answer 19

see the choice now?

Answer 20

\(\bf x^2 + 18x = 0\implies (x^2 + 18x) = 0\\ \quad \\
\implies (x^2 + 18x+{\color{red}{ 9 }}^2) -{\color{red}{ 9 }}^2= 0\\ \quad \\\implies (x+9)^2-9^2=0\implies (x+9)^2=81\)