25=10t-0.83t^2
Solve for t
25=10t-0.83t^2
25 = 10t - 0.6889t
25 = 9.3111t
15.6889 = t
How did you get 0.6889
0.83 t squared
0.83t * 0.83t = 0.6889t
To solve for t in the equation 25 = 10t - 0.83t^2, we can follow these steps:
Step 1: Rearrange the equation to set it equal to zero by subtracting 25 from both sides:
-0.83t^2 + 10t - 25 = 0
Step 2: Check if we can factor the quadratic equation. However, in this case, factoring might not work easily since the coefficients are not simple integers.
Step 3: We can solve the quadratic equation by using the quadratic formula, given by:
t = (-b ± √(b^2 - 4ac)) / (2a)
In this case, the equation is in the form: at^2 + bt + c = 0, where:
a = -0.83
b = 10
c = -25
Step 4: Plug the values of a, b, and c into the quadratic formula and simplify:
t = (-(10) ± √((10)^2 - 4(-0.83)(-25))) / (2(-0.83))
t = (-10 ± √(100 + 83)) / -1.66
Step 5: Simplify further by calculating the values inside the square root and performing any necessary calculations:
t = (-10 ± √(183)) / -1.66
Step 6: Approximate the square root of 183 as a decimal:
t ≈ (-10 ± 13.52774927) / -1.66
Step 7: Now, calculate the two possible values for t by using both the positive and negative square root:
t ≈ (-10 + 13.52774927) / -1.66 or t ≈ (-10 - 13.52774927) / -1.66
Step 8: Simplify each expression separately:
t ≈ 3.5277 / -1.66 or t ≈ -23.5277 / -1.66
Step 9: Lastly, calculate the decimal approximations for t:
t ≈ -2.1233 or t ≈ 14.1701
Therefore, the solutions to the equation 25 = 10t - 0.83t^2 are approximately t = -2.1233 and t ≈ 14.1701.