(x+4)(x+9)=0

Jasonbradley

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Jun 16, 2024

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Solving the Quadratic Equation: (x+4)(x+9) = 0

This equation represents a quadratic equation in factored form. To solve for the values of x that satisfy the equation, we can utilize 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.

Applying the Zero Product Property

1. Set each factor equal to zero:

   • (x + 4) = 0
   • (x + 9) = 0

2. Solve for x in each equation:

   • x + 4 = 0 => x = -4
   • x + 9 = 0 => x = -9

Solutions

Therefore, the solutions to the quadratic equation (x+4)(x+9) = 0 are:

• x = -4
• x = -9

These solutions represent the points where the graph of the quadratic function intersects the x-axis. In other words, they are the x-intercepts of the parabola.

Expanding the Equation

While we solved the equation in its factored form, it's useful to understand the relationship between the factored form and the standard form of the quadratic equation. Expanding the given equation, we get:

(x+4)(x+9) = x² + 13x + 36 = 0

This standard form (ax² + bx + c = 0) reveals that the quadratic equation has a leading coefficient of 1, a coefficient of 13 for the linear term, and a constant term of 36. It's important to note that solving for x using the factored form is generally more efficient than using the quadratic formula or completing the square for this specific equation.