Solve for x in the equation X^2 - 8X + 41 = 0

The equation has two solutions for x:

x₁ = (8 + 10i) / 2

x₂ = (8 - 10i) / 2

Step-by-step explanation:

Let's use the quadratic formula for solving for x in the equation:

X^2 - 8X + 41 = 0

x² - 8x + 41 = 0

Let's recall that the quadratic formula is:

x = - b + / - (√b² - 4ac) / 2a

Replacing with the real values, we have:

x = 8 + / - (√-8² - 4 * 1 * 41) / 2 * 1

x = 8 + / - (√64 - 164) / 2

x = 8 + / - (√-100) / 2

x = 8 + / - (√-1 * 100) / 2

Let's recall that √-1 = i

x = 8 + / - 10i/2

x₁ = (8 + 10i) / 2

x₂ = (8 - 10i) / 2