Solution - Equations reducible to quadratic form

Rearrange:

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

                     10*p^4-(p^2+25)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (2•5p4) -  (p2 + 25)  = 0 

Step  2  :

Trying to factor by splitting the middle term

 2.1     Factoring  10p⁴-p²-25 

The first term is,  10p⁴  its coefficient is  10 .
The middle term is,  -p²  its coefficient is  -1 .
The last term, "the constant", is  -25 

Step-1 : Multiply the coefficient of the first term by the constant   10 • -25 = -250 

Step-2 : Find two factors of  -250  whose sum equals the coefficient of the middle term, which is   -1 .

Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored

Equation at the end of step  2  :

  10p4 - p2 - 25  = 0 

Step  3  :

Solving a Single Variable Equation :

Equations which are reducible to quadratic :

 3.1     Solve   10p⁴-p²-25 = 0

This equation is reducible to quadratic. What this means is that using a new variable, we can rewrite this equation as a quadratic equation Using  o , such that  o = p²  transforms the equation into :
 10o²-o-25 = 0

Solving this new equation using the quadratic formula we get two real solutions :
   1.6319  or  -1.5319

Now that we know the value(s) of  o , we can calculate  p  since  p  is  √ o  

Doing just this we discover that the solutions of
   10p⁴-p²-25 = 0
  are either : 
   p =√ 1.632 = 1.27747  or :
   p =√ 1.632 = -1.27747  or :
   p =√-1.532 = 0.0 + 1.23771 i  or :
   p =√-1.532 = 0.0 - 1.23771 i

Four solutions were found :

1.  p =√-1.532 = 0.0 - 1.23771 i
2.  p =√-1.532 = 0.0 + 1.23771 i
3.  p =√ 1.632 = -1.27747
4.  p =√ 1.632 = 1.27747