Question
Consider the quadratic equation below.
x
2
+
6
x
+
9
=
0
x
2
+6x+9=0
x
2
+
6
x
+
9
=
0
x
2
+6x+9=0
Answers
GPT-4o mini
The given quadratic equation is:
\[
x^2 + 6x + 9 = 0
\]
This equation can be factored. Notice that it is a perfect square trinomial:
\[
(x + 3)^2 = 0
\]
To find the solutions, we can set the factored form equal to zero:
\[
(x + 3)^2 = 0
\]
Taking the square root of both sides gives:
\[
x + 3 = 0
\]
Solving for \(x\):
\[
x = -3
\]
Since this is a perfect square, it has one repeated solution (also known as a double root). Therefore, the solution to the quadratic equation \(x^2 + 6x + 9 = 0\) is:
\[
x = -3
\]
If you need any further explanations or examples, feel free to ask!
\[
x^2 + 6x + 9 = 0
\]
This equation can be factored. Notice that it is a perfect square trinomial:
\[
(x + 3)^2 = 0
\]
To find the solutions, we can set the factored form equal to zero:
\[
(x + 3)^2 = 0
\]
Taking the square root of both sides gives:
\[
x + 3 = 0
\]
Solving for \(x\):
\[
x = -3
\]
Since this is a perfect square, it has one repeated solution (also known as a double root). Therefore, the solution to the quadratic equation \(x^2 + 6x + 9 = 0\) is:
\[
x = -3
\]
If you need any further explanations or examples, feel free to ask!