(x%2B6)%3D0.jpeg "(2x-1)(x+6)=0")
Solving the Equation (2x-1)(x+6) = 0
This equation represents a quadratic equation in factored form. To solve for x, we can utilize the Zero Product Property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
Here's how we can solve the equation:
1. Set each factor equal to zero:
- 2x - 1 = 0
- x + 6 = 0
2. Solve for x in each equation:
-
2x - 1 = 0
- Add 1 to both sides: 2x = 1
- Divide both sides by 2: x = 1/2
-
x + 6 = 0
- Subtract 6 from both sides: x = -6
Therefore, the solutions to the equation (2x-1)(x+6) = 0 are x = 1/2 and x = -6.
What does this mean graphically?
This equation represents a parabola. The solutions we found (x = 1/2 and x = -6) are the x-intercepts of the parabola. These are the points where the parabola intersects the x-axis.
In summary, by applying the Zero Product Property, we efficiently solved the factored quadratic equation and found the two solutions, which represent the x-intercepts of the corresponding parabola.