Final answer:
To solve the quadratic equation x² + 2x + 5 = 0, we can use the quadratic formula. The solutions to the equation are -1 + 2.236i and -1 - 2.236i.
Step-by-step explanation:
To solve the quadratic equation x² + 2x + 5 = 0, we can use the quadratic formula. The formula states that for an equation of the form ax² + bx + c = 0, the solutions or roots can be calculated using the formula:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 1, b = 2, and c = 5. Plugging these values into the quadratic formula, we get:
x = (-2 ± sqrt(2² - 4(1)(5))) / 2(1)
Simplifying further, we find that the solutions to the quadratic equation are:
x ≈ -1 + 2.236i (complex number) and x ≈ -1 - 2.236i (complex number)