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Solve x3 – 25
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1 Answer

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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

User PSchuette
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