Answer: x = ∛25 = 2.9240
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