(x%5E2-49)%3D0.jpeg "(x+7)(x^2-49)=0")
Solving the Equation (x+7)(x^2-49)=0
This equation represents a polynomial equation that can be solved using the Zero Product Property. This property states that if the product of two or more factors is zero, then at least one of the factors must be zero.
Let's break down the steps to solve this equation:
1. Identify the Factors
We have two factors:
- (x + 7)
- (x² - 49)
2. Apply the Zero Product Property
For the product of these factors to be zero, either:
- (x + 7) = 0
- (x² - 49) = 0
3. Solve for x in each equation
For (x + 7) = 0:
- Subtract 7 from both sides: x = -7
For (x² - 49) = 0:
- Add 49 to both sides: x² = 49
- Take the square root of both sides: x = ±7
4. Combine the Solutions
Therefore, the solutions to the equation (x+7)(x^2-49)=0 are:
- x = -7
- x = 7
Conclusion
By applying the Zero Product Property and solving for x in each factor, we successfully found the three solutions to the equation. This demonstrates the power of factoring and the Zero Product Property in solving polynomial equations.