30=-16t^2+55t+4

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Solution for 30=-16t^2+55t+4 equation:


Simplifying
30 = -16t2 + 55t + 4

Reorder the terms:
30 = 4 + 55t + -16t2

Solving
30 = 4 + 55t + -16t2

Solving for variable 't'.

Combine like terms: 30 + -4 = 26
26 + -55t + 16t2 = 4 + 55t + -16t2 + -4 + -55t + 16t2

Reorder the terms:
26 + -55t + 16t2 = 4 + -4 + 55t + -55t + -16t2 + 16t2

Combine like terms: 4 + -4 = 0
26 + -55t + 16t2 = 0 + 55t + -55t + -16t2 + 16t2
26 + -55t + 16t2 = 55t + -55t + -16t2 + 16t2

Combine like terms: 55t + -55t = 0
26 + -55t + 16t2 = 0 + -16t2 + 16t2
26 + -55t + 16t2 = -16t2 + 16t2

Combine like terms: -16t2 + 16t2 = 0
26 + -55t + 16t2 = 0

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

Divide each side by '16'.
1.625 + -3.4375t + t2 = 0

Move the constant term to the right:

Add '-1.625' to each side of the equation.
1.625 + -3.4375t + -1.625 + t2 = 0 + -1.625

Reorder the terms:
1.625 + -1.625 + -3.4375t + t2 = 0 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + -3.4375t + t2 = 0 + -1.625
-3.4375t + t2 = 0 + -1.625

Combine like terms: 0 + -1.625 = -1.625
-3.4375t + t2 = -1.625

The t term is -3.4375t.  Take half its coefficient (-1.71875).
Square it (2.954101563) and add it to both sides.

Add '2.954101563' to each side of the equation.
-3.4375t + 2.954101563 + t2 = -1.625 + 2.954101563

Reorder the terms:
2.954101563 + -3.4375t + t2 = -1.625 + 2.954101563

Combine like terms: -1.625 + 2.954101563 = 1.329101563
2.954101563 + -3.4375t + t2 = 1.329101563

Factor a perfect square on the left side:
(t + -1.71875)(t + -1.71875) = 1.329101563

Calculate the square root of the right side: 1.152866672

Break this problem into two subproblems by setting 
(t + -1.71875) equal to 1.152866672 and -1.152866672.

Subproblem 1

t + -1.71875 = 1.152866672 Simplifying t + -1.71875 = 1.152866672 Reorder the terms: -1.71875 + t = 1.152866672 Solving -1.71875 + t = 1.152866672 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = 1.152866672 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = 1.152866672 + 1.71875 t = 1.152866672 + 1.71875 Combine like terms: 1.152866672 + 1.71875 = 2.871616672 t = 2.871616672 Simplifying t = 2.871616672

Subproblem 2

t + -1.71875 = -1.152866672 Simplifying t + -1.71875 = -1.152866672 Reorder the terms: -1.71875 + t = -1.152866672 Solving -1.71875 + t = -1.152866672 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.71875' to each side of the equation. -1.71875 + 1.71875 + t = -1.152866672 + 1.71875 Combine like terms: -1.71875 + 1.71875 = 0.00000 0.00000 + t = -1.152866672 + 1.71875 t = -1.152866672 + 1.71875 Combine like terms: -1.152866672 + 1.71875 = 0.565883328 t = 0.565883328 Simplifying t = 0.565883328

Solution

The solution to the problem is based on the solutions from the subproblems. t = {2.871616672, 0.565883328}

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