X^2+8x+12=0

Question

Solving the equation

Answer 1

A easy way to learn how to do this is the quadratic formula and all you have to do is sing it! The formula is -B(plus or minus)(square root) B²-4(A)(C) all over 2(A) to the song Row, Row, Row Your Boat. First you'll have to classify the letters.

A=1, because there is ALWAYS a invisible 1 in front of an X if there is no number.

B=8

and C=12

So your formula should now look like this

-8+or-(Square Root sign)8²-4(1)(12)/2(1) OR LIKE THIS

-8+or-(Square Root sign)8²-4(1)(12
                           2

Then You work it out !

-8+or-(Square Root sign)64-48
                    2

-8+or-(Square Root sign)16
                 2

This is where you break down the square root of 16, which is 4, and bring it out.

-8+or-4
     2

Now you break it up into 2 problems

-8+4 = -4 which reduces to X=-2 and -8-4 = -12 which reduces to X=-6
   2       2                                            2        2

Now plug your answers in:

-2²+8(-2)+12=0 ; 4-16+12=0 CORRECT

-6²+8(-6)+12=0 ; 36-48+12=0 CORRECT

And that's how you get it using the quadratic formula! it's a fun and easy way to do problems that = to zero because even if a letter is missing you can always sub zero. As you do it more and more the song is easier to remember and you get faster at it! I hope this helps!

Answer 2

This is an exercise in factoring and solving for all possible solutions to the equation. The highest order exponent, in this equation X² , determines there are exactly 2 solutions. This simply means that there are exactly 2 values for X that you could plug into the equation and it would be true. One must factor to determine these solutions to the equation.

X² + 8X + 12 = 0   Factoring identifies the binomials whose product equals the polynomial.

The second + sign tells you the signs of the binomials are alike, the first plus sign tells you they are both positive.

(X + some number)(X + another number) = X² + 8X + 12 = 0

What 2 numbers multiply together to equal 12 and add together to equal 8? 6 and 2.

(X+2)(X+6) = X² + 8X + 12 = 0

for the product of any 2 numbers to equal zero, one OR the other must equal zero. Setting both equal to zero and solving for X provides the 2 values of X that will make the Polynomial true when entered into the original equation.

X+2 = 0 , X = -2

X+6 = 0, X = -6

Plug em in and check your answer.

X=-2, (-2)² + 8(-2) + 12 = 0 <------> 4 - 16 + 12 = 0   true statement

X=-6, (-6)² + 8(-6) + 12 = 0 <------> 36 - 48 + 12 = 0 true statement again

 

 

 

Answer 3

x² + 8 · x + 12 = 0
       ↑         ↑  
    (6+2)    6*2

(x + 6)(x + 2) = 0 ---> x₁ = -6
                                  x₂ = -2