x(2-x-3)%3D0.jpeg "(1/2+2x)x(2 X-3)=0")
Solving the Equation (1/2 + 2x) * (2x - 3) = 0
This equation is a quadratic equation in disguise. To solve it, we can use the Zero Product Property. This property states that if the product of two or more factors is equal to zero, then at least one of the factors must be equal to zero.
Here's how we can solve the equation:
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Identify the factors: In this case, the factors are (1/2 + 2x) and (2x - 3).
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Set each factor equal to zero:
- (1/2 + 2x) = 0
- (2x - 3) = 0
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Solve for x in each equation:
- For (1/2 + 2x) = 0:
- 2x = -1/2
- x = -1/4
- For (2x - 3) = 0:
- 2x = 3
- x = 3/2
- For (1/2 + 2x) = 0:
Therefore, the solutions to the equation (1/2 + 2x) * (2x - 3) = 0 are x = -1/4 and x = 3/2.
Understanding the Solution
The solutions represent the x-intercepts of the graph of the quadratic function. These are the points where the graph crosses the x-axis. Since the product of the two factors is zero, it means that at least one of the factors is zero, leading to the graph intersecting the x-axis at the points corresponding to these solutions.
Conclusion
By applying the Zero Product Property, we effectively solved the quadratic equation (1/2 + 2x) * (2x - 3) = 0, finding two distinct solutions: x = -1/4 and x = 3/2. This approach demonstrates a fundamental technique for solving equations involving products of factors.