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Solving the Quadratic Equation: (6x-5)(x+2)=0
This equation represents a quadratic equation in factored form. To solve for x, we can use 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 apply this to our equation:
Step 1: Set each factor equal to zero.
- 6x - 5 = 0
- x + 2 = 0
Step 2: Solve each equation for x.
- For 6x - 5 = 0:
- Add 5 to both sides: 6x = 5
- Divide both sides by 6: x = 5/6
- For x + 2 = 0:
- Subtract 2 from both sides: x = -2
Therefore, the solutions to the equation (6x-5)(x+2)=0 are x = 5/6 and x = -2.
Explanation:
- These solutions represent the x-intercepts of the parabola represented by the equation. In other words, these are the points where the graph of the parabola crosses the x-axis.
- The factored form of the equation helps us visualize the solutions more easily. Each factor corresponds to a specific x-intercept.
In conclusion, we have successfully solved the quadratic equation (6x-5)(x+2)=0 by utilizing the Zero Product Property. We have identified the two solutions, x = 5/6 and x = -2, which are also the x-intercepts of the parabola represented by this equation.