Completing the Square & the Quadratic Formula Practice

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Question
Using the quadratic formula, find the solution to x2+6x+9=0
.(1 point)
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Answer 1

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:

\[ x = -3 \]