Question

Solve x3 – 25 Please HELP

Answer 1

There is no solution it’s in final form

Answer 2

Answer:  x = ∛25 = 2.9240

Step-by-step explanation:x3-25=0

Reformatting the input :

Changes made to your input should not affect the solution:

(1): "x3"   was replaced by   "x^3".

Step by step solution :

Step  1  :

Trying to factor as a Difference of Cubes:

1.1      Factoring:  x3-25

Theory : A difference of two perfect cubes,  a3 - b3 can be factored into

             (a-b) • (a2 +ab +b2)

Proof :  (a-b)•(a2+ab+b2) =

           a3+a2b+ab2-ba2-b2a-b3 =

           a3+(a2b-ba2)+(ab2-b2a)-b3 =

           a3+0+0+b3 =

           a3+b3

Check :  25  is not a cube !!

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

Polynomial Roots Calculator :

1.2    Find roots (zeroes) of :       F(x) = x3-25

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  -25.

The factor(s) are:

of the Leading Coefficient :  1

of the Trailing Constant :  1 ,5 ,25

   P      Q      P/Q      F(P/Q)       Divisor

      -1         1          -1.00          -26.00      

      -5         1          -5.00          -150.00      

      -25         1         -25.00         -15650.00      

      1         1          1.00          -24.00      

      5         1          5.00          100.00      

      25         1          25.00         15600.00      

Polynomial Roots Calculator found no rational roots

Equation at the end of step  1  :

 x3 - 25  = 0

Step  2  :

Solving a Single Variable Equation :

2.1      Solve  :    x3-25 = 0

Add  25  to both sides of the equation :

                     x3 = 25

When two things are equal, their cube roots are equal. Taking the cube root of the two sides of the equation we get:  

                     x  =  ∛ 25  

The equation has one real solution

This solution is  x = ∛25 = 2.9240