38=-16t^2+40t+5

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Solution for 38=-16t^2+40t+5 equation:


Simplifying
38 = -16t2 + 40t + 5

Reorder the terms:
38 = 5 + 40t + -16t2

Solving
38 = 5 + 40t + -16t2

Solving for variable 't'.

Combine like terms: 38 + -5 = 33
33 + -40t + 16t2 = 5 + 40t + -16t2 + -5 + -40t + 16t2

Reorder the terms:
33 + -40t + 16t2 = 5 + -5 + 40t + -40t + -16t2 + 16t2

Combine like terms: 5 + -5 = 0
33 + -40t + 16t2 = 0 + 40t + -40t + -16t2 + 16t2
33 + -40t + 16t2 = 40t + -40t + -16t2 + 16t2

Combine like terms: 40t + -40t = 0
33 + -40t + 16t2 = 0 + -16t2 + 16t2
33 + -40t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
33 + -40t + 16t2 = 0

Begin completing the square.  Divide all terms by
16 the coefficient of the squared term: 

Divide each side by '16'.
2.0625 + -2.5t + t2 = 0

Move the constant term to the right:

Add '-2.0625' to each side of the equation.
2.0625 + -2.5t + -2.0625 + t2 = 0 + -2.0625

Reorder the terms:
2.0625 + -2.0625 + -2.5t + t2 = 0 + -2.0625

Combine like terms: 2.0625 + -2.0625 = 0.0000
0.0000 + -2.5t + t2 = 0 + -2.0625
-2.5t + t2 = 0 + -2.0625

Combine like terms: 0 + -2.0625 = -2.0625
-2.5t + t2 = -2.0625

The t term is -2.5t.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5t + 1.5625 + t2 = -2.0625 + 1.5625

Reorder the terms:
1.5625 + -2.5t + t2 = -2.0625 + 1.5625

Combine like terms: -2.0625 + 1.5625 = -0.5
1.5625 + -2.5t + t2 = -0.5

Factor a perfect square on the left side:
(t + -1.25)(t + -1.25) = -0.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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