If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the value of x? (2

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Question: If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the value of x? (2023)

Options:

Correct Answer: -1

Exam Year: 2023

Solution:

The equation can be factored as (x + 1)^2 = 0, giving the root x = -1.

If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the value of x? (2023)

If the quadratic equation x^2 + 2x + 1 = 0 is solved, what is the value of x? (2023)

Step 1: Start with the quadratic equation x^2 + 2x + 1 = 0.
Step 2: Recognize that this equation can be factored. Look for two numbers that multiply to 1 (the constant term) and add to 2 (the coefficient of x).
Step 3: The numbers that work are 1 and 1, so we can write the equation as (x + 1)(x + 1) = 0.
Step 4: This can be simplified to (x + 1)^2 = 0.
Step 5: To find the value of x, set (x + 1) equal to 0: x + 1 = 0.
Step 6: Solve for x by subtracting 1 from both sides: x = -1.

Quadratic Equations – Understanding how to solve quadratic equations through factoring, completing the square, or using the quadratic formula.
Factoring – Recognizing that the quadratic can be expressed as a perfect square.