solve the following equation by factoring, 6x^2 - 24 = 0

Question

thanks guys!!! i appreciate your help so much :)

Answer 1

a^2 - b^2 = (a - b)(a + b)

6x^2 - 24 = 0

6(x^2 - 4) = 0

x^2 - 2^2 = 0

(x - 2)(x + 2) = 0

x₁ = - 2
x₂ = 2

Answer 2

Hi Selema;

6x²-24=0

For the FOIL...

FIRST must be (6x)(x) or (3x)(2x).

OUTER and INNER must add-up to 0x.

LAST must be (12)(2) or (2)(12) or (6)(4) or (4)(6) or (3)(8) or (8)(3) and one number must be negative.

 

(6x-12)(x+2)=0

Let's FOIL...

FIRST...(6x)(x)=6x²

OUTER...(6x)(2)=12x

INNER...(-12)(x)=-12x

LAST...(-12)(2)=-24

6x²+12x-12x-24=0

6x²-24=0

 

For the factored equation to result in zero, either parenthetical equation must equal zero.

6x-12=0

6x=12

x=2

 

x+2=0

x=-2

 

x is -2 or 2

 

or

(6x+12)(x-2)=0

I flipped the + and - sign.

The results are the same...

6x+12=0

6x=-12

x=-2

 

x-2=0

x=2

 

x is -2 or 2