Solution - Reducing fractions to their lowest terms

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "17.28" was replaced by "(1728/100)".

Step by step solution :

Step  1  :

            432
 Simplify   ———
            25 

Equation at the end of step  1  :

   432           
  (——— • x2) +  2730  = 0 
   25            

Step  2  :

Equation at the end of step  2  :

  432x2    
  ————— +  2730  = 0 
   25      

Step  3  :

Rewriting the whole as an Equivalent Fraction :

 3.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  25  as the denominator :

            2730     2730 • 25
    2730 =  ————  =  —————————
             1          25    

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:

 432x2 + 2730 • 25     432x2 + 68250
 —————————————————  =  —————————————
        25                  25      

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   432x² + 68250  =   6 • (72x² + 11375) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 72x² + 11375
Polynomial Roots Calculator is a set of methods aimed at finding values of  x  for which   F(x)=0  

Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  x  which can be expressed as the quotient of two integers

The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient

In this case, the Leading Coefficient is  72  and the Trailing Constant is  11375.

 The factor(s) are:

of the Leading Coefficient :  1,2 ,3 ,4 ,6 ,8 ,9 ,12 ,18 ,24 , etc
 of the Trailing Constant :  1 ,5 ,7 ,13 ,25 ,35 ,65 ,91 ,125 ,175 , etc

 Let us test ....

Note - For tidiness, printing of 195 checks which found no root was suppressed

Polynomial Roots Calculator found no rational roots

Equation at the end of step  4  :

  6 • (72x2 + 11375)
  ——————————————————  = 0 
          25        

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:

  6•(72x2+11375)
  —————————————— • 25 = 0 • 25
        25      

Now, on the left hand side, the  25  cancels out the denominator, while, on the right hand side, zero times anything is still zero.

The equation now takes the shape :
   6  •  (72x²+11375)  = 0

Equations which are never true :

 5.2      Solve :    6   =  0

This equation has no solution.
A a non-zero constant never equals zero.

Solving a Single Variable Equation :

 5.3      Solve  :    72x²+11375 = 0 

 Subtract  11375  from both sides of the equation : 
                      72x² = -11375
Divide both sides of the equation by 72:
                     x² = -11375/72 = -157.986
 
 When two things are equal, their square roots are equal. Taking the square root of the two sides of the equation we get:  
                      x  =  ± √ -11375/72  

 In Math,  i  is called the imaginary unit. It satisfies   i²  =-1. Both   i   and   -i   are the square roots of   -1 

Accordingly,  √ -11375/72  =
                    √ -1• 11375/72   =
                    √ -1 •√  11375/72   =
                    i •  √ 11375/72

The equation has no real solutions. It has 2 imaginary, or complex solutions.

                      x=  0.0000 +12.5693 i 
                      x=  0.0000 -12.5693 i 

Two solutions were found :

1.   x=  0.0000 -12.5693 i 
   
2.   x=  0.0000 +12.5693 i