Question

Solve x2 + 9x + 9 = 0.

quantity of negative 9 plus or minus 3 square root of 5 all over 2
quantity of 9 plus or minus 3 square root of 5 all over 2
quantity of negative 9 plus or minus square root of 117 all over 2
quantity of 9 plus or minus square root of 117 all over 2

Answer 1

To solve the quadratic equation \( x^2 + 9x + 9 = 0 \), we can use the quadratic formula:

\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

where \( a = 1 \), \( b = 9 \), and \( c = 9 \).

First, we calculate the discriminant, \( b^2 - 4ac \):

\[
b^2 = 9^2 = 81
\]
\[
4ac = 4 \cdot 1 \cdot 9 = 36
\]
\[
b^2 - 4ac = 81 - 36 = 45
\]

Now, we substitute back into the quadratic formula:

\[
x = \frac{-9 \pm \sqrt{45}}{2 \cdot 1}
\]
\[
x = \frac{-9 \pm \sqrt{45}}{2}
\]

Next, we simplify \( \sqrt{45} \):

\[
\sqrt{45} = \sqrt{9 \cdot 5} = 3\sqrt{5}
\]

Now we substitute this back:

\[
x = \frac{-9 \pm 3\sqrt{5}}{2}
\]

So the solutions for the equation \( x^2 + 9x + 9 = 0 \) are:

\[
x = \frac{-9 + 3\sqrt{5}}{2} \quad \text{and} \quad x = \frac{-9 - 3\sqrt{5}}{2}
\]

Based on your options, the correct answer is:

\[
\text{Quantity of} \; \text{-9 plus or minus 3 square root of 5 all over 2}
\]