Solution - Other Factorizations

Reformatting the input :

Changes made to your input should not affect the solution:

 (1): "t1"   was replaced by   "t^1". 

Rearrange:

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

                     22*t^10-(98)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (2•11t10) -  98  = 0 

Step  2  :

Step  3  :

Pulling out like terms :

 3.1     Pull out like factors :

   22t¹⁰ - 98  =   2 • (11t¹⁰ - 49) 

Trying to factor as a Difference of Squares :

 3.2      Factoring:  11t¹⁰ - 49 

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 :  11  is not a square !!

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

Equation at the end of step  3  :

  2 • (11t10 - 49)  = 0 

Step  4  :

Equations which are never true :

 4.1      Solve :    2   =  0

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

Solving a Single Variable Equation :

 4.2      Solve  :    11t¹⁰-49 = 0 

 Add  49  to both sides of the equation : 
                      11t¹⁰ = 49
Divide both sides of the equation by 11:
                     t¹⁰ = 49/11 = 4.455
                     t  =  10th root of (49/11) 

 The equation has two real solutions  
 These solutions are  t = 10th root of ( 4.455) = ± 1.16113  
 

Two solutions were found :