Question

3n^2 - 2n - 12 = 4 - in completing the square

Answer 1

Answer:

STEP

1

:

Equation at the end of step 1

(22n2 - 2n) - 12 = 0

STEP

2

:

STEP

3

:

Pulling out like terms

3.1 Pull out like factors :

4n2 - 2n - 12 = 2 • (2n2 - n - 6)

Trying to factor by splitting the middle term

3.2 Factoring 2n2 - n - 6

The first term is, 2n2 its coefficient is 2 .

The middle term is, -n its coefficient is -1 .

The last term, "the constant", is -6

Step-1 : Multiply the coefficient of the first term by the constant 2 • -6 = -12

Step-2 : Find two factors of -12 whose sum equals the coefficient of the middle term, which is -1 .

-12 + 1 = -11

-6 + 2 = -4

-4 + 3 = -1 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -4 and 3

2n2 - 4n + 3n - 6

Step-4 : Add up the first 2 terms, pulling out like factors :

2n • (n-2)

Add up the last 2 terms, pulling out common factors :

3 • (n-2)

Step-5 : Add up the four terms of step 4 :

(2n+3) • (n-2)

Answer 2

Step-by-step explanation:

$\tt \red{ \implies3n {}^{2} −2n−12−4=0}$

$\tt \pink{ \implies3n {}^{2} −2n−16=0}$

1. Multiply the coefficient of the first term by the constant term.

3×−16=−48

2.Ask: Which two numbers add up to −2 and multiply to −48?

6 and −8

3.Split −2n as the sum of 6n and −8n.

$\sf\blue{\implies 3{n}^{2}+6n-8n-16.}$

•Factor out common terms in the first two terms, then in the last two terms.

3n(n+2)-8(n+2)=0

•Factor out the common term n+2n+2.

(n+2)(3n-8)=0

•When n+2=0 or 3n−8=0

•Solve each of the 2 equations above.

$\red{\boxed{\boxed{\boxed{\boxed{{\tt\orange{n=-2,\frac{8}{3}}}}}}}}$