K=1/2kx^2

find the value of X

x=± 2

=±1.4142

x=0

Explanation: If this does not help then I'm sorry.

STEP

1

:

           1

Simplify   —

           2

Equation at the end of step

1

:

        1

 k -  ((— • k) • x2)  = 0  

        2

STEP

2

:

Equation at the end of step 2

      kx2

 k -  ———  = 0  

       2  

STEP

3

:

Rewriting the whole as an Equivalent Fraction

3.1   Subtracting a fraction from a whole

Rewrite the whole as a fraction using  2  as the denominator :

         k     k • 2

    k =  —  =  —————

         1       2  

Equivalent fraction : The fraction thus generated looks different but has the same value as the whole

Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator

Adding fractions that have a common denominator :

3.2       Adding up the two equivalent fractions

Add the two equivalent fractions which now have a common denominator

Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

k • 2 - (kx2)     2k - kx2

—————————————  =  ————————

      2              2    

STEP

4

:

Pulling out like terms

4.1     Pull out like factors :

  2k - kx2  =   -k • (x2 - 2)  

Trying to factor as a Difference of Squares:

4.2      Factoring:  x2 - 2  

Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B)

Proof :  (A+B) • (A-B) =

        A2 - AB + BA - B2 =

        A2 - AB + AB - B2 =

        A2 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check : 2 is not a square !!

Ruling : Binomial can not be factored as the difference of two perfect squares.

Equation at the end of step

4

:

 -k • (x2 - 2)

 —————————————  = 0  

       2      

STEP

5

:

When a fraction equals zero

5.1    When a fraction equals zero ...

Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.

Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.

Here's how:

 -k•(x2-2)

 ————————— • 2 = 0 • 2

     2    

Now, on the left hand side, the  2  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :

  -k  •  (x2-2)  = 0

Theory - Roots of a product :

5.2    A product of several terms equals zero.  

When a product of two or more terms equals zero, then at least one of the terms must be zero.  

We shall now solve each term = 0 separately  

In other words, we are going to solve as many equations as there are terms in the product  

Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation:

5.3      Solve  :    -k = 0  

Multiply both sides of the equation by (-1) :  k = 0

Solving a Single Variable Equation:

5.4      Solve  :    x2-2 = 0  

Add  2  to both sides of the equation :  

                     x2 = 2

When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  

                     x  =  ± √ 2  

The equation has two real solutions  

These solutions are  x = ± √2 = ± 1.4142  

Three solutions were found :

x = ± √2 = ± 1.4142

k = 0

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