Final answer:
To solve 100t² - 80t + 16 = 0, use the quadratic formula. The discriminant is zero, indicating one solution. The simplified solution is t = 2/5.
Step-by-step explanation:
To solve the quadratic equation 100t² - 80t + 16 = 0 for t, we will apply the quadratic formula:
t = −b ± √(b² - 4ac) / (2a)
For our equation, a = 100, b = -80, and c = 16. Plugging these values into the quadratic formula, we have:
t = −(-80) ± √((-80)² - 4∙100∙16) / (2∙100)
Simplifying the expression under the square root (√(b² - 4ac)):
t = 80 ± √(6400 - 6400) / 200
Since √(6400 - 6400) = 0, the equation becomes:
t = 80 / 200
Therefore, t = 0.4 which simplifies to 2/5 when expressed as a fraction. This is the only solution since the discriminant (b² - 4ac) is zero, indicating that both solutions are the same.
The correct solution in simplest form is t = 2/5.