Questions: Solve the equation using the quadratic formula. x^2 + 7x + 9 = 0 The solution set is

Solution Steps

To solve the quadratic equation $x^2 + 7x + 9 = 0$ using the quadratic formula, we identify the coefficients $a = 1$, $b = 7$, and $c = 9$. The quadratic formula is given by:

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

We will calculate the discriminant $b^2 - 4ac$ and then use it to find the two possible values for $x$.

For the quadratic equation $x^2 + 7x + 9 = 0$, we identify the coefficients:

• $a = 1$
• $b = 7$
• $c = 9$

We calculate the discriminant using the formula $D = b^2 - 4ac$: $$D = 7^2 - 4 \cdot 1 \cdot 9 = 49 - 36 = 13$$

Using the quadratic formula $x = \frac{{-b \pm \sqrt{D}}}{2a}$, we find the two solutions: $$x_1 = \frac{{-7 + \sqrt{13}}}{2 \cdot 1} = \frac{{-7 + \sqrt{13}}}{2}$$ $$x_2 = \frac{{-7 - \sqrt{13}}}{2 \cdot 1} = \frac{{-7 - \sqrt{13}}}{2}$$

Calculating the numerical values: $$x_1 \approx -1.6972 \quad \text{and} \quad x_2 \approx -5.3028$$

Final Answer