Solution - Power equations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "x1"   was replaced by   "x^1". 

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

                2*(1/4*x)^3-(-27/4*(x^1/2)^3)=0 

Step by step solution :

Step  1  :

            x
 Simplify   —
            2

Equation at the end of step  1  :

       1           27  x
  (2•((—•x)3))-(0-(——•(—3)))  = 0 
       4           4   2

Step  2  :

Equation at the end of step  2  :

       1           27 x3
  (2•((—•x)3))-(0-(——•——))  = 0 
       4           4  23

Step  3  :

            27
 Simplify   ——
            4 

Equation at the end of step  3  :

       1           27 x3
  (2•((—•x)3))-(0-(——•——))  = 0 
       4           4  23

Step  4  :

Raising to a Power :

 4.1    2²  multiplied by  2³   = 2^{(2 + 3)} = 2⁵

Equation at the end of step  4  :

       1          27x3
  (2•((—•x)3))-(0-————)  = 0 
       4           32 

Step  5  :

            1
 Simplify   —
            4

Equation at the end of step  5  :

         1            -27x3
  (2 • ((— • x)3)) -  —————  = 0 
         4             32  

Step  6  :

 6.1     4 = 2² (4)³ = (2²)³ = 2⁶

Equation at the end of step  6  :

       x3     -27x3
  (2 • ——) -  —————  = 0 
       26      32  

Step  7  :

Dividing exponents :

 7.1    2¹   divided by   2⁶   = 2^{(1 - 6)} = 2^(-5) = ¹/_2⁵

Equation at the end of step  7  :

  x3    -27x3
  —— -  —————  = 0 
  32     32  

Step  8  :

Adding fractions which have a common denominator :

 8.1       Adding fractions which have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:

 x3 - (-27x3)     28x3
 ————————————  =  ————
      32           32 

Equation at the end of step  8  :

  28x3
  ————  = 0 
   32 

Step  9  :

When a fraction equals zero :

 9.1    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:

  28x3
  ———— • 32 = 0 • 32
   32 

Now, on the left hand side, the  32  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   28x³  = 0

Solving a Single Variable Equation :

 9.2      Solve  :    28x³ = 0 

 Divide both sides of the equation by 28:
                     x³ = 0
When two things are equal, their cube roots are equal. Taking the cube root of the two sides of the equation we get:  
                      x  =  ∛ 0  

 Any root of zero is zero. This equation has one solution which is  x = 0

One solution was found :