Final answer:
To solve the quadratic equation 16-20s^2+18s+17=0 by factoring, rearrange the equation to get 0 on one side. Factor the quadratic expression and set each factor equal to zero to solve for s. The solutions are s = 1/4 and s = -17/5.
Step-by-step explanation:
To solve the quadratic equation 16-20s^2+18s+17=0 by factoring, we need to find two values of s that when substituted into the equation, make it equal to zero.
Step 1: Rearrange the equation to get 0 on one side:
(16-20s^2) + 18s + 17 = 0
Step 2: Factor the quadratic expression:
(4s-1)(-5s-17) = 0
Step 3: Set each factor equal to zero and solve for s:
4s-1 = 0 -> 4s = 1 -> s = 1/4
-5s-17 = 0 -> -5s = 17 -> s = -17/5
Therefore, the solutions to the quadratic equation are s = 1/4 and s = -17/5.