Question

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

Answer 1

The equation has two solutions for x:

x₁ = (8 + 10i)/2

x₂ = (8 - 10i)/2

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