500(3)=-16t^2+175t+500

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Solution for 500(3)=-16t^2+175t+500 equation: 


Simplifying
500(3) = -16t2 + 175t + 500

Multiply 500 * 3
1500 = -16t2 + 175t + 500

Reorder the terms:
1500 = 500 + 175t + -16t2

Solving
1500 = 500 + 175t + -16t2

Solving for variable 't'.

Combine like terms: 1500 + -500 = 1000
1000 + -175t + 16t2 = 500 + 175t + -16t2 + -500 + -175t + 16t2

Reorder the terms:
1000 + -175t + 16t2 = 500 + -500 + 175t + -175t + -16t2 + 16t2

Combine like terms: 500 + -500 = 0
1000 + -175t + 16t2 = 0 + 175t + -175t + -16t2 + 16t2
1000 + -175t + 16t2 = 175t + -175t + -16t2 + 16t2

Combine like terms: 175t + -175t = 0
1000 + -175t + 16t2 = 0 + -16t2 + 16t2
1000 + -175t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
1000 + -175t + 16t2 = 0

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

Divide each side by '16'.
62.5 + -10.9375t + t2 = 0

Move the constant term to the right:

Add '-62.5' to each side of the equation.
62.5 + -10.9375t + -62.5 + t2 = 0 + -62.5

Reorder the terms:
62.5 + -62.5 + -10.9375t + t2 = 0 + -62.5

Combine like terms: 62.5 + -62.5 = 0.0
0.0 + -10.9375t + t2 = 0 + -62.5
-10.9375t + t2 = 0 + -62.5

Combine like terms: 0 + -62.5 = -62.5
-10.9375t + t2 = -62.5

The t term is -10.9375t.  Take half its coefficient (-5.46875).
Square it (29.90722656) and add it to both sides.

Add '29.90722656' to each side of the equation.
-10.9375t + 29.90722656 + t2 = -62.5 + 29.90722656

Reorder the terms:
29.90722656 + -10.9375t + t2 = -62.5 + 29.90722656

Combine like terms: -62.5 + 29.90722656 = -32.59277344
29.90722656 + -10.9375t + t2 = -32.59277344

Factor a perfect square on the left side:
(t + -5.46875)(t + -5.46875) = -32.59277344

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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