Introduction

In mathematics, solving equations is a fundamental skill. This article delves into the solution of a specific algebraic equation, x3 - x x2x - xx. We will explore various methods to find the value of x, including traditional algebraic manipulation and factorization techniques. Understanding these methods can help improve problem-solving skills in mathematics.

Solving the Equation x3 - x x2x - xx

Algorithm and Step-by-Step Solution

Given the equation: x3 - x x2x - xx

Step 1: Simplify the given equation Step 2: Simplify further for clarity Step 3: Isolate x terms Step 4: Solve for x

Begin by simplifying the given equation:

x3 - x x2x - xx

First, we can see that x2x x3. Hence, we rewrite the equation as:

x3 - x x3 - xx

Step 2: Simplification and Further Clarity

To further simplify, let's add x to both sides of the equation:

x3 - x x x3 - xx x

This simplifies to:

x3 x3 - xx x

Step 3: Isolate x Terms

Notice that x3-x3 cancels out:

0 -xx x

Multiplying both sides by -1 for clarity:

0 xx - x

Factor out x:

0 x(x - 1)

Step 4: Solve for x

Setting each factor equal to zero:

x 0 x - 1 0

Thus, the solutions are:

x 0, 1

Conclusion

The final solutions to the equation x3 - x x2x - xx are x 0 and x 1. Understanding the step-by-step process of solving such equations can greatly enhance one's algebraic problem-solving skills. For further practice and in-depth explanations, refer to the Math Problem Solver (Cymath).

Additional Resources

For additional learning and practice, you might want to refer to the following websites and resources:

Mathalicious Khan Academy Algebra Algebra Calculator