Solve Quadratic Equation: x² + 3x + 7 = 0 in Standard Form

Solve the following equation:

$x^2+3x+7=0$

To solve the quadratic equation $x^2 + 3x + 7 = 0$, we will use the quadratic formula:

• Quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.
• Identify the coefficients: $a = 1$, $b = 3$, $c = 7$.
• Calculate the discriminant: $D = b^2 - 4ac = 3^2 - 4(1)(7) = 9 - 28 = -19$.

The discriminant $D = -19$ is negative. This indicates that there are no real roots to the equation. Quadratic equations with negative discriminants have complex solutions.

Therefore, the given quadratic equation $x^2 + 3x + 7 = 0$ has no solutions in the real number system, and we conclude that:

No solution.