(x+5)2=0 Standard Form

Jasonbradley

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Jun 17, 2024

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Solving the Equation (x+5)² = 0

This equation is a quadratic equation in disguise! Here's how to solve it and understand its standard form:

Understanding the Equation:

• (x+5)²: This represents the square of the binomial (x+5). In other words, it's (x+5) multiplied by itself: (x+5)(x+5).

Expanding and Simplifying:

1. Expand the square: (x+5)(x+5) = x² + 5x + 5x + 25
2. Combine like terms: x² + 10x + 25 = 0

Standard Form of a Quadratic Equation:

The standard form of a quadratic equation is ax² + bx + c = 0, where 'a', 'b', and 'c' are constants.

Our simplified equation (x² + 10x + 25 = 0) is already in standard form.

Solving for x:

1. Factoring: Notice that the left side of the equation is a perfect square trinomial: (x + 5)² = 0.
2. Take the square root: √(x + 5)² = √0
3. Simplify: x + 5 = 0
4. Solve for x: x = -5

Solution:

The solution to the equation (x+5)² = 0 is x = -5.

Important Note: This equation has a single solution, which means the graph of the quadratic function would intersect the x-axis at only one point, making it a "double root".