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Completing the Square & the Quadratic Formula Practice
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Using the quadratic formula, find the solution to x2+6x+9=0
.(1 point)
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Answers
GPT-4o mini
To solve the quadratic equation \( x^2 + 6x + 9 = 0 \) using the quadratic formula, we first identify the coefficients \( a \), \( b \), and \( c \) from the standard form of a quadratic equation \( ax^2 + bx + c = 0 \).
In this case:
- \( a = 1 \)
- \( b = 6 \)
- \( c = 9 \)
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Now let's plug in the values of \( a \), \( b \), and \( c \):
1. Calculate the discriminant \( b^2 - 4ac \):
\[
b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot 9 = 36 - 36 = 0
\]
2. Substitute the values into the quadratic formula:
\[
x = \frac{-6 \pm \sqrt{0}}{2 \cdot 1} = \frac{-6 \pm 0}{2} = \frac{-6}{2} = -3
\]
Since the discriminant is zero, there is one repeated solution.
Therefore, the solution to the equation \( x^2 + 6x + 9 = 0 \) is:
\[
x = -3
\]
In this case:
- \( a = 1 \)
- \( b = 6 \)
- \( c = 9 \)
The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Now let's plug in the values of \( a \), \( b \), and \( c \):
1. Calculate the discriminant \( b^2 - 4ac \):
\[
b^2 - 4ac = 6^2 - 4 \cdot 1 \cdot 9 = 36 - 36 = 0
\]
2. Substitute the values into the quadratic formula:
\[
x = \frac{-6 \pm \sqrt{0}}{2 \cdot 1} = \frac{-6 \pm 0}{2} = \frac{-6}{2} = -3
\]
Since the discriminant is zero, there is one repeated solution.
Therefore, the solution to the equation \( x^2 + 6x + 9 = 0 \) is:
\[
x = -3
\]