To complete the square for the quadratic expression -16t^2 + 40t + 1.5, follow these steps:
Step 1: Divide the entire expression by the coefficient of the squared term (-16) to make the leading coefficient 1:
-16t^2 + 40t + 1.5 becomes t^2 - (40/(-16))t + (1.5/(-16))
Step 2: Focus on the quadratic term and the linear term. Take half of the coefficient of the linear term, square it, and add/subtract it to the expression:
t^2 - (40/(-16))t + (1.5/(-16))
= t^2 - 2.5t + (1.5/(-16)) + (2.5/(-16))
Step 3: Simplify the expression inside the parentheses:
= t^2 - 2.5t + (-0.09375) + (-0.15625)
Step 4: Rearrange the terms:
= (t^2 - 2.5t + (-0.09375)) + (-0.15625)
Step 5: Factor the perfect square trinomial inside the parentheses:
= (t - 1.25)^2 - 0.15625
Therefore, the quadratic expression -16t^2 + 40t + 1.5, when completed, becomes (t - 1.25)^2 - 0.15625.