Final answer:
To solve the corrected quadratic equation 5x^2 - 8x + 5 = 0, the quadratic formula is used and yields two complex roots: x = 4/5 + 3/5 i and x = 4/5 - 3/5 i.
Step-by-step explanation:
To solve the given quadratic equation 5.12 - 8x + 5 = 0, we first correct the equation, noticing that it's likely a typo and the correct form most likely should be 5x2 - 8x + 5 = 0. This assumption is based on the common structure of quadratic equations and we proceed under this assumption. To solve a quadratic equation of the form ax2 + bx + c = 0, you can use the quadratic formula:
x = -b ± √(b² - 4ac) / (2a)
Applying the quadratic formula to the corrected equation 5x2 - 8x + 5 = 0, with a = 5, b = -8, and c = 5, we get:
x = (8 ± √((-8)² - 4(5)(5))) / (2(5))
Simplifying further:
x = (8 ± √(64 - 100)) / 10
x = (8 ± √(-36)) / 10
x = (8 ± 6i) / 10
The solutions are complex numbers. Thus, in the simplest form, the solutions (roots) of the quadratic equation are x = 4/5 + 3/5 i and x = 4/5 - 3/5 i.