help me understand how to slove these equations please?

Question

Solve Xsquared-4=12
:
Xsquared-4-12=0
Xsquared-6x-2x-12=0
X(X-6)+2(X-6)=0
(X-6) (X+2) = 0
X-6=0 X+2=0
answer: X=6 X= -2

i dont really get what's going on here.i try to follow but i dont get it.can someone please help me understand whats going on or help me with an alternative method to get the right answers?

Answer 1

Solve Xsquared-4=12

Xsquared-4-12=0
Xsquared-16=0
(X-4)(X+4)=0
X-4=0 or X+4=0
answer: X=4 or X= -4

Answer 2

They're factoring these by using the distributive rule in reverse. If we start with x(x-6) + 2(x-6), this becomes (x-6)(x+2). If the product of these is zero, then that means either x-6 is zero or x+2 is zero (when you multiply two numbers together and get zero, that means one of the numbers was zero to begin with). So this means x = 6 or -2.

However, this doesn't follow the original problem. You wrote x^2 - 4 = 12 on the first line. This means x^2 = 16, so x= -4 or 4. Then on the next line you wrote x^2 - 6x - 2x - 12 = 0. I don't see how this follows. Even if it was x^2 - 4x = 12 you originally meant to write, this would come out to x^2 - 6x + 2x - 12 on the left, not x^2 - 6x - 2x - 12.

Answer 3

x^2 - 4 = 12
x^2 = 12+4 = 16
x = +/- 4 Just take the square root of both sides

x^2-4x-12 = 0 <-- you left out the x after the 4
(x-6)(x+2)=0 Factor the above
Set each factor to 0 getting :
x-6=0 --> x = 6
x+2 = 0 --> x = -2

Answer 4

but the answer you have is wrong
if x=6 so 6^2-4=12,
36-4 =12
32=12.
That particular equation is easier to solve this way:
x^2 - 4 = 12
x^2 = 12 + 4 [because moving a number from one side of an equation to another reverses its sign so -4 becomes +4]
x^2 = 16
so what multiplied by itself = 16? Well 4 is the obvious answer, but remember that two negative numbers multiplied together equal a positive so your answer is +4 or -4

Answer 5

Xsquared-4x=12
Xsquared-4x -12=0
factorize (x-6 )(x+2) = 0
(x-6 ) =0 or (x+2) = 0
x = 6 or x = -2

Answer 6

x^2-4=12
x^2=4+12=16
x=+-4 [square rooting both sides]