(x-7)(x+2)=0

Jasonbradley

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Jun 17, 2024

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Solving the Equation: (x-7)(x+2) = 0

This equation is a simple quadratic equation, and we can solve it 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.

Here's how we can solve it:

1. Set each factor equal to zero:

   • x - 7 = 0
   • x + 2 = 0

2. Solve for x in each equation:

   • x = 7
   • x = -2

Therefore, the solutions to the equation (x-7)(x+2) = 0 are x = 7 and x = -2.

Understanding the Solution

These solutions represent the points where the graph of the quadratic equation crosses the x-axis. The equation (x-7)(x+2) = 0 is equivalent to the equation y = (x-7)(x+2). The solutions to the equation represent the x-intercepts of the parabola.

Verification

We can verify our solutions by substituting them back into the original equation:

• For x = 7: (7-7)(7+2) = 0 * 9 = 0, which is true.
• For x = -2: (-2-7)(-2+2) = -9 * 0 = 0, which is also true.

This confirms that our solutions are correct.

Conclusion

By applying the Zero Product Property, we successfully solved the equation (x-7)(x+2) = 0 and found the two solutions: x = 7 and x = -2. These solutions represent the x-intercepts of the corresponding parabola.