Answer:
  
 x = ± ∜175 = ± 3.6371
 
Step-by-step explanation:
Rearrange:
Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :
                     x^4-(175)=0 
Step by step solution :
STEP
1
:
Trying to factor as a Difference of Squares:
 1.1      Factoring:  x4-175 
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 : 175 is not a square !!
Ruling : Binomial can not be factored as the difference of two perfect squares.
Polynomial Roots Calculator :
 1.2    Find roots (zeroes) of :       F(x) = x4-175
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  -175.
 The factor(s) are:
of the Leading Coefficient :  1
 of the Trailing Constant :  1 ,5 ,7 ,25 ,35 ,175
 Let us test ....
  	P    Q    P/Q    F(P/Q)    	Divisor
      -1       1        -1.00        -174.00    	
      -5       1        -5.00        450.00    	
      -7       1        -7.00        2226.00    	
      -25       1       -25.00       390450.00    	
      -35       1       -35.00       1500450.00    	
      -175       1       -175.00       937890450.00    	
      1       1        1.00        -174.00    	
      5       1        5.00        450.00    	
      7       1        7.00        2226.00    	
      25       1        25.00       390450.00    	
      35       1        35.00       1500450.00    	
      175       1       175.00       937890450.00    	
Polynomial Roots Calculator found no rational roots
Equation at the end of step
1
:
  x4 - 175  = 0 
STEP
2
:
Solving a Single Variable Equation:
 2.1      Solve  :    x4-175 = 0 
 Add  175  to both sides of the equation : 
                      x4 = 175
                     x  =  ∜ 175  
 The equation has two real solutions  
 These solutions are  x = ± ∜175 = ± 3.6371  
 
Two solutions were found :
 x = ± ∜175 = ± 3.6371