(x+3)(x+4)=0 In Standard Form

Jasonbradley

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Jun 16, 2024

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Solving Quadratic Equations: (x+3)(x+4)=0

This equation is already factored, making it easy to solve. Here's how to break it down:

Understanding the Zero Product Property

The Zero Product Property states that if the product of two or more factors is zero, then at least one of the factors must be zero. In this case, we have:

(x + 3)(x + 4) = 0

This means either (x + 3) = 0 or (x + 4) = 0.

Solving for x

1. Solve for x + 3 = 0: Subtract 3 from both sides: x = -3

2. Solve for x + 4 = 0: Subtract 4 from both sides: x = -4

Therefore, the solutions to the equation (x + 3)(x + 4) = 0 are x = -3 and x = -4.

Standard Form

To express the equation in standard form, we need to expand the factored form and set it equal to zero:

(x + 3)(x + 4) = 0

Expanding the left side:

x² + 4x + 3x + 12 = 0

Combining like terms:

x² + 7x + 12 = 0

This is the standard form of the quadratic equation.

Key Points

• The factored form makes it easy to identify the solutions directly.
• The standard form is useful for other methods of solving quadratic equations, such as the quadratic formula or completing the square.