x^2-8x+12= 0 can any 1 help me solve this quardratic equation? plz show steps?

Answer 1

two numbers that multiply to 12 and add up to -8

-6 and -2

(x-6)(x-2)

x= 6 or 2

Answer 2

The simplest way to find the roots (if you can't do it visually as demonstrated above) is to use the formula

a is the coefficient of the x²
b is the coefficient of the x
c is the number with no x

x = (-b ± √(b² - 4ac))/2a

In your example

a = 1
b = -8 (note: negative 8 as you're subtracting not adding 8x)
c = 12

x = (-(-8) ± √((-8)² - 4(1)(12)))/2(1)
= (8 ± √(64 - 48))/2
= (8 ± √16)/2
= (8 ± 4)/2

The ± means you now need to split it into two equations
x = (8 + 4)/2 = 12/2 = 6
x = (8 - 4)/2 = 4/2 = 2

So your answer is x = {2, 6}

Answer 3

x^2 - 8x + 12 = 0

You need two numbers which add up to -8, and multiply to give you + 12. These numbers are - 6 and - 2.
Factorize to get:

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

The answer is the negative of the two values above, 6 and 2. Don't forget that there are always 2 answers in this type of quadratic equation.

Therefore, x = 6 or x = 2

Answer 4

First: multiply the 1st & 3rd coefficient to get "12." Find two numbers that give you "12" when multiplied & "-8" (2nd/middle coefficient) when added/subtracted. The numbers are "-6 & -2"

Sec: rewrite the expression with the new middle coefficients...

x^2 - 6x - 2x + 12 = 0

Third: factor - when you have 4 terms, group "like" terms....

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

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

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

Fourth: solve the x-variables - set both parenthesis to "0"...

a. x - 6 = 0
*Add "6" to both sides to isolate "x" on one side...

x - 6 + 6 = 0 + 6
x = 6

b. x - 2 = 0
*Add "2" to both sides...

x - 2 + 2 = 0 + 2
x = 2

Solution: 2 and 6

Answer 5

Quadratic Formula

x = - b ± √b² - 4ac / 2a

x² - 8x + 12

a = 1

b = - 8

c = 12

- - - - - - - - -

x = - (- 8) ± √(- 8)² - 4(1)(12) / 2(1)

x = 8 ± √64 - 48 / 2

x = 8 ± √16 / 2

x = (8 ± 4) / 2

- - - - - - -

Solving for +

x = 8 + 4 / 2

x = 12 / 2

x = 6

The answer is x = 6

- - - - - - - -

solving for -

x = 8 - 4 / 2

x = 4 / 2

x = 2

The answer is x = 2

- - - - - - - - - -s-

Answer 6

x^2 - 8x + 12 = 0
(x - 6)(x - 2) = 0
x - 6 = 0 or x - 2 = 0
x = 6 or x = 2
QED

Answer 7

factorize
(x-6)(x-2)=0
x-6=0 x-2=0
x=6 x=2
x={2,6}