Answer :
To solve the quadratic equation \( x^2 + 2x + 1 = 0 \) numerically, we need to find the values of \( x \) for which the equation holds true. Let's follow the steps to solve this problem:
1. Identify the quadratic equation:
[tex]\[ x^2 + 2x + 1 = 0 \][/tex]
2. Rewrite the equation and factorize it (if possible):
Notice that the quadratic expression can be factored:
[tex]\[ x^2 + 2x + 1 = (x + 1)^2 \][/tex]
3. Set the factored form equal to zero:
[tex]\[ (x + 1)^2 = 0 \][/tex]
4. Solve for \( x \) by taking the square root of both sides:
[tex]\[ x + 1 = 0 \][/tex]
5. Isolate \( x \):
[tex]\[ x = -1 \][/tex]
So, the solution to the quadratic equation is \( x = -1 \).
Given the solution, let's check which of the given options includes \( x = -1 \):
- Option A: \( x = -1 \) (correct)
- Option B: \( x = 1 \) or \( x = -3 \) (incorrect)
- Option C: \( x = 3 \) (incorrect)
- Option D: \( x = 2 \) or \( x = -1 \) (incorrect)
The correct answer that matches the solution \( x = -1 \) is:
A
1. Identify the quadratic equation:
[tex]\[ x^2 + 2x + 1 = 0 \][/tex]
2. Rewrite the equation and factorize it (if possible):
Notice that the quadratic expression can be factored:
[tex]\[ x^2 + 2x + 1 = (x + 1)^2 \][/tex]
3. Set the factored form equal to zero:
[tex]\[ (x + 1)^2 = 0 \][/tex]
4. Solve for \( x \) by taking the square root of both sides:
[tex]\[ x + 1 = 0 \][/tex]
5. Isolate \( x \):
[tex]\[ x = -1 \][/tex]
So, the solution to the quadratic equation is \( x = -1 \).
Given the solution, let's check which of the given options includes \( x = -1 \):
- Option A: \( x = -1 \) (correct)
- Option B: \( x = 1 \) or \( x = -3 \) (incorrect)
- Option C: \( x = 3 \) (incorrect)
- Option D: \( x = 2 \) or \( x = -1 \) (incorrect)
The correct answer that matches the solution \( x = -1 \) is:
A
