Final answer:
To solve the quadratic equation 10x^2 - 27x + 5 = 0, you can use the quadratic formula. The solutions for x are 2.5 and 0.2.
Step-by-step explanation:
To solve the quadratic equation 10x^2 - 27x + 5 = 0, we can use the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / (2a)
From the given equation, a = 10, b = -27, and c = 5.
Plugging these values into the quadratic formula gives:
x = (-(-27) ± √((-27)^2 - 4(10)(5))) / (2(10))
Simplifying further:
x = (27 ± √(729 - 200)) / 20
x = (27 ± √529) / 20
x = (27 ± 23) / 20
Therefore, x can be either:
x = (27 + 23) / 20 = 50 / 20 = 2.5
Or:
x = (27 - 23) / 20 = 4 / 20 = 0.2