Question

question 7 of 10
what is the solution to the following equation?
$x^2 + 5x + 7 = 0$
a. $x = \frac{-5\pm\sqrt{-3}}{2}$
b. $x = \frac{-5\pm\sqrt{53}}{2}$
c. $x = \frac{3\pm\sqrt{25}}{2}$
d. $x = \frac{-3\pm\sqrt{-7}}{2}$

Explanation:

Step1: Recall Quadratic Formula

For a quadratic equation \( ax^2 + bx + c = 0 \), the solutions are given by \( x=\frac{-b\pm\sqrt{b^2 - 4ac}}{2a} \).
Here, \( a = 1 \), \( b = 5 \), \( c = 7 \).

Step2: Calculate Discriminant (\( b^2 - 4ac \))

Substitute \( a = 1 \), \( b = 5 \), \( c = 7 \) into \( b^2 - 4ac \):
\( 5^2-4\times1\times7 = 25 - 28=-3 \).

Step3: Apply Quadratic Formula

Substitute \( a = 1 \), \( b = 5 \), and discriminant \( -3 \) into the formula:
\( x=\frac{-5\pm\sqrt{-3}}{2} \).

Answer:

A. \( x = \frac{-5\pm\sqrt{-3}}{2} \)