Can someone help me with this one? 2X^2 + 16 = 12x?

Hi,

2x² + 16 = 12x
2x² - 12x + 16 = 0
2(x² - 6x + 8) = 0
2(x - 4)(x - 2) = 0
x - 4 = 0
x = 4

x - 2 = 0
x = 2

The answers are x = 2 and x = 4.

I hope that helps!! :-)

2x^2 - 12 x +16 = 0
2 [x^2 - 6x +8] = 0
solving you will gt 2 [(x-4)(x-2)]=0
x=4 or 2

2x^2 + 16 = 12x
2x^2 - 12x + 16 = 0
(2x - 4)(x - 4) = 0

2x - 4 = 0
2x = 4
x = 4/2
x = 2

x - 4 = 0
x = 4

∴ x = 2 or 4

you question can be written as
2x^2-12x+16=0
this is a quadratic equation which can be solved
2x^2-4x-8x+16=0
2x(x-2)-8(x-2)=0
=(2x-8)(x-2)=0


therefore
either
2x-8=0 or x-2 =0

solving in these for x



x=4 or x=2

x² - 6x + 8 = 0
(x - 4)(x - 2) = 0
x = 2 , x = 4

2x^2 + 16 = 12x

2x^2 - 12x + 16 = 0 (Subtract 12x from both sides)

2(x^2 - 6x + 8) = 0 (Factor out a 2, and since the other side equals 0, you can just ignore the 2)

(x - 4) (x - 2) = 0 (This is just factoring- note that -4 times -2 is 8 and -4x plus -2x is -6x)

Since x - 4 times x - 2 equal 0, one of them can equal 0, because 0 times anything is 0, so you set
x - 4 = 0
x = 4

AND

x - 2 = 0
x = 2

So x can be either 2 or 4

Subtract 12x on both sides to get 2x^2 - 12x + 16 = 0
Now, use the Quadratic formula to solve for x
[-b +/- sqrt(b^2 - 4ac)] / 2a

a is 2, b is -12, and c is 16. Plug it in the Quadratic formula to get ...

[-(-12) +/- sqrt (-12)^2 - 4(2)(16)] / 2(2)
[12 +/- sqrt(144 - 128)] / 4.
144 - 128 = 16 and the square root of 16 is 4 so..
(12 +/- 4) / 4

You'll have two x's since you are solving a polynomial with a degree of 2.

x1 = (12 + 4)/(4) = 4
x2 = (12 - 4)/(4) = 2

A much easier method is factoring the equation.
2x^2 - 12x + 16 is the same thing as 2(x^2 - 6x + 8) which can also be reduced to 2(x -4)(x - 2). Then, what numbers can you plug into x to make this = to 0? If factoring is hard for you, stick with the Quadratic Method as it's always guaranteed to work.

x=1.51

WORK:
SQUARE ROOT OF 2X^2 =1.41X
SO THE PROBLEM WOULD BE 1.41X+16=12X
YOU SUBTRACT 1.41X FROM 12X TO GET 10.59X
DIVIDE 16 BY 10.59 TO GET X BY ITSELF
WHICH MAKES X EQUAL 1.51

2x^2+16=12x
x^2+8=6x
x^2-6x+8=0
x^2-2x-4x+8=0
x(x-2)-4(x-2)=0
(x-4)(x-2)=0


x=4 ; x=2

2x^2+16=12x
-12x -12x

2x^2-12x+16

Answer: (2x-4)(x-4)