20 = 37t - 16t^2
if you are supposed to solve for t: subtract 20 to the other side, then either factor and set both factors equal to zero, or use the quadratic formula on the newly obtained -16t^2 + 37t - 20.
b^2-4ac = 89 is not a perfect square so it is not going to get factored. Quadratic equation is necessary.
To solve the equation 20 = 37t - 16t^2, we can rearrange the terms to form a quadratic equation. Let's bring all the terms to one side of the equation:
16t^2 - 37t + 20 = 0
This quadratic equation is in the form of ax^2 + bx + c = 0, where a = 16, b = -37, and c = 20. Now, we can solve this equation using factorization, completing the square, or the quadratic formula.
First, let's try to factorize the equation. We need to find two numbers that multiply to give us ac (16 * 20 = 320) and add up to give us b (-37). After examining the factors of 320, we can see that -5 and -32 satisfy these conditions:
(16t - 5)(t - 4) = 0
By setting each factor equal to zero, we get:
16t - 5 = 0 or t - 4 = 0
Solving for t in each equation, we find:
16t = 5 or t = 4
t = 5/16 or t = 4
So, the solutions to the equation 20 = 37t - 16t^2 are t = 5/16 and t = 4.