Question

What is the solution to the following equation?

x^2 + 3x + 7 = 0
A) x = -3 + 7
B) x = -3 - 19
C) x = 33 + 25
D) x = -3 + 427

Answer 1

The solution for the quadratic equation x² + 3x + 7 = 0 requires using the quadratic formula. After applying the formula, we find that the equation has complex solutions because the discriminant (9 - 28) is negative, leading to an imaginary number within the square root.

Step-by-step explanation:

The equation provided is a quadratic equation of the form ax²+bx+c = 0. In this case, we cannot simply factor the equation, so we must use the quadratic formula to find the solutions for x. The quadratic formula is:

x = −b ± √(b² − 4ac) / (2a)

For the given equation x² + 3x + 7 = 0, a = 1, b = 3, and c = 7. Plugging these into the formula, we get:

x = −(3) ± √((3)² − 4 × 1 × 7) / (2 × 1

This simplifies to:

x = −(3) ± √(9 − 28) / 2

Since 9 − 28 is negative, this means we will have complex solutions. After calculating, we find that the discriminant is negative, hence the solutions are not real numbers. The options given A through D are not the correct solutions for this equation.