Simplify the square root of 30/20

ANSWER:   5x2 - 5x + 26

                  ———————

                                5    

Step-by-step explanation:   />      Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x2"   was replaced by   "x^2".

(2): "2.2" was replaced by "(22/10)".

Step by step solution :

Step  1  :

           3

Simplify   —

           1

Equation at the end of step  1  :

  22                    

 (—— -  x) +  ((x2) +  3)

  10                    

Step  2  :

           11

Simplify   ——

           5

Equation at the end of step  2  :

  11          

 (—— -  x) +  (x2 + 3)

  5          

Step  3  :

Rewriting the whole as an Equivalent Fraction :

3.1   Subtracting a whole from a fraction

Rewrite the whole as a fraction using  5  as the denominator :

        x     x • 5

   x =  —  =  —————

        1       5  

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:

11 - (x • 5)     11 - 5x

————————————  =  ———————

     5              5  

Equation at the end of step  3  :

 (11 - 5x)    

 ————————— +  (x2 + 3)

     5        

Step  4  :

Rewriting the whole as an Equivalent Fraction :

4.1   Adding a whole to a fraction

Rewrite the whole as a fraction using  5  as the denominator :

             x2 + 3     (x2 + 3) • 5

   x2 + 3 =  ——————  =  ————————————

               1             5      

Polynomial Roots Calculator :

4.2    Find roots (zeroes) of :       F(x) = x2 + 3

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  1  and the Trailing Constant is  3.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,3

Let us test

   P      Q      P/Q      F(P/Q)      Divisor

      -1         1          -1.00          4.00      

      -3         1          -3.00          12.00      

      1         1          1.00          4.00      

      3         1          3.00          12.00      

Polynomial Roots Calculator found no rational roots

Adding fractions that have a common denominator :

4.3       Adding up the two equivalent fractions

(11-5x) + (x2+3) • 5     5x2 - 5x + 26

————————————————————  =  —————————————

         5                     5      

Trying to factor by splitting the middle term

4.4     Factoring  5x2 - 5x + 26

The first term is,  5x2  its coefficient is  5 .

The middle term is,  -5x  its coefficient is  -5 .

The last term, "the constant", is  +26

Step-1 : Multiply the coefficient of the first term by the constant   5 • 26 = 130

Step-2 : Find two factors of  130  whose sum equals the coefficient of the middle term, which is   -5 .

     -130     +    -1     =    -131  

     -65     +    -2     =    -67  

     -26     +    -5     =    -31  

     -13     +    -10     =    -23  

     -10     +    -13     =    -23  

     -5     +    -26     =    -31  

     -2     +    -65     =    -67  

     -1     +    -130     =    -131  

     1     +    130     =    131  

     2     +    65     =    67  

     5     +    26     =    31  

     10     +    13     =    23  

     13     +    10     =    23  

     26     +    5     =    31  

     65     +    2     =    67  

     130     +    1     =    131  

Observation : No two such factors can be found !!

Conclusion : Trinomial can not be factored

Final result :

 5x2 - 5x + 26

 —————————————

       5      

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