Solution - Nonlinear equations

Rearrange:

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

                     x^4-(-12)=0 

Step by step solution :

Step  1  :

Polynomial Roots Calculator :

 1.1    Find roots (zeroes) of :       F(x) = x⁴+12
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  12.

 The factor(s) are:

of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,2 ,3 ,4 ,6 ,12

 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step  1  :

  x4 + 12  = 0 

Step  2  :

Solving a Single Variable Equation :

 2.1      Solve  :    x⁴+12 = 0 

 Subtract  12  from both sides of the equation : 
                      x⁴ = -12
                     x  =  ∜ -12  

 The equation has no real solutions. It has 4 imaginary, or complex solutions.

                      x=  1.3161 + 1.3161 i 
                      x=  -1.3161 + 1.3161 i 
                      x=  -1.3161 - 1.3161 i 
                      x=  1.3161 - 1.3161 i 

Four solutions were found :

1.   x=  1.3161 - 1.3161 i 
   
2.   x=  -1.3161 - 1.3161 i 
   
3.   x=  -1.3161 + 1.3161 i 
   
4.   x=  1.3161 + 1.3161 i