We can solve the quadratic equation 2x² - 8x + 5 = 0 by using the quadratic formula, which states that for an equation of the form ax² + bx + c = 0, the solutions are given by:
x = (-b ± sqrt(b² - 4ac)) / 2a
In this case, a = 2, b = -8, and c = 5. Substituting these values into the formula, we get:
x = (-(-8) ± sqrt((-8)² - 4(2)(5))) / (2(2))
x = (8 ± sqrt(64 - 40)) / 4
x = (8 ± sqrt(24)) / 4
x = (8 ± 2sqrt(6)) / 4
Simplifying the expression by factoring out a common factor of 2 in the numerator and denominator, we get:
x = (2(4 ± sqrt(6))) / (2(2))
x = 4 ± sqrt(6)
Therefore, the solutions to the equation 2x² - 8x + 5 = 0 are:
x = 4 + sqrt(6) or x = 4 - sqrt(6)