Answer: t₁ = (-35 + √73) / (-32)
t₂ = (-35 - √73) / (-32)
Explanation:
To solve the quadratic equation:
0 = -18 + 35t - 16t^2
You can rearrange it into standard quadratic form, which is:
0 = -16t^2 + 35t - 18
Now, you can attempt to factor it or use the quadratic formula to find the values of t that satisfy this equation. Let's use the quadratic formula:
The quadratic formula is given by:
t = (-b ± √(b² - 4ac)) / (2a)
In this equation, a = -16, b = 35, and c = -18. Plug these values into the formula:
t = (-(35) ± √((35)² - 4(-16)(-18))) / (2(-16))
Now, calculate:
t = (-35 ± √(1225 - 1152)) / (-32)
t = (-35 ± √73) / (-32)
So, the solutions for t are:
t₁ = (-35 + √73) / (-32)
t₂ = (-35 - √73) / (-32)
These are the two values of t that satisfy the equation.