The quadratic equation x^2 + 6x + 9 = 0 can be expressed in the form of (x + a)^

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Question: The quadratic equation x^2 + 6x + 9 = 0 can be expressed in the form of (x + a)^2. What is the value of a? (2022)

Options:

Correct Answer: 3

Exam Year: 2022

Solution:

The equation can be factored as (x + 3)^2 = 0, hence a = 3.

The quadratic equation x^2 + 6x + 9 = 0 can be expressed in the form of (x + a)^2. What is the value of a? (2022)

The quadratic equation x^2 + 6x + 9 = 0 can be expressed in the form of (x + a)^2. What is the value of a? (2022)

Step 1: Start with the quadratic equation x^2 + 6x + 9 = 0.
Step 2: Notice that the equation can be factored. We want to express it in the form (x + a)^2.
Step 3: Look for two identical numbers that add up to 6 (the coefficient of x) and multiply to 9 (the constant term).
Step 4: The numbers 3 and 3 fit this because 3 + 3 = 6 and 3 * 3 = 9.
Step 5: Therefore, we can write the equation as (x + 3)(x + 3) = 0.
Step 6: This simplifies to (x + 3)^2 = 0.
Step 7: From the expression (x + a)^2, we see that a = 3.

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