Solution - Nonlinear equations

Rearrange:

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

                     5*(3*x^4)-(-10)=0 

Step by step solution :

Step  1  :

Equation at the end of step  1  :

  (5 • 3x4) -  -10  = 0 

Step  2  :

Equation at the end of step  2  :

  (5•3x4) -  -10  = 0 

Step  3  :

Step  4  :

Pulling out like terms :

 4.1     Pull out like factors :

   15x⁴ + 10  =   5 • (3x⁴ + 2) 

Polynomial Roots Calculator :

 4.2    Find roots (zeroes) of :       F(x) = 3x⁴ + 2
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  3  and the Trailing Constant is  2.

 The factor(s) are:

of the Leading Coefficient :  1,3
 of the Trailing Constant :  1 ,2

 Let us test ....

Polynomial Roots Calculator found no rational roots

Equation at the end of step  4  :

  5 • (3x4 + 2)  = 0 

Step  5  :

Equations which are never true :

 5.1      Solve :    5   =  0

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

Solving a Single Variable Equation :

 5.2      Solve  :    3x⁴+2 = 0 

 Subtract  2  from both sides of the equation : 
                      3x⁴ = -2
Divide both sides of the equation by 3:
                     x⁴ = -2/3 = -0.667
                     x  =  ∜ -2/3  

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

                      x=  0.6389 + 0.6389 i 
                      x=  -0.6389 + 0.6389 i 
                      x=  -0.6389 - 0.6389 i 
                      x=  0.6389 - 0.6389 i 

Four solutions were found :

1.   x=  0.6389 - 0.6389 i 
   
2.   x=  -0.6389 - 0.6389 i 
   
3.   x=  -0.6389 + 0.6389 i 
   
4.   x=  0.6389 + 0.6389 i