100=37t-2t^2

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Solution for 100=37t-2t^2 equation:


Simplifying
100 = 37t + -2t2

Solving
100 = 37t + -2t2

Solving for variable 't'.

Reorder the terms:
100 + -37t + 2t2 = 37t + -37t + -2t2 + 2t2

Combine like terms: 37t + -37t = 0
100 + -37t + 2t2 = 0 + -2t2 + 2t2
100 + -37t + 2t2 = -2t2 + 2t2

Combine like terms: -2t2 + 2t2 = 0
100 + -37t + 2t2 = 0

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

Divide each side by '2'.
50 + -18.5t + t2 = 0

Move the constant term to the right:

Add '-50' to each side of the equation.
50 + -18.5t + -50 + t2 = 0 + -50

Reorder the terms:
50 + -50 + -18.5t + t2 = 0 + -50

Combine like terms: 50 + -50 = 0
0 + -18.5t + t2 = 0 + -50
-18.5t + t2 = 0 + -50

Combine like terms: 0 + -50 = -50
-18.5t + t2 = -50

The t term is -18.5t.  Take half its coefficient (-9.25).
Square it (85.5625) and add it to both sides.

Add '85.5625' to each side of the equation.
-18.5t + 85.5625 + t2 = -50 + 85.5625

Reorder the terms:
85.5625 + -18.5t + t2 = -50 + 85.5625

Combine like terms: -50 + 85.5625 = 35.5625
85.5625 + -18.5t + t2 = 35.5625

Factor a perfect square on the left side:
(t + -9.25)(t + -9.25) = 35.5625

Calculate the square root of the right side: 5.963430221

Break this problem into two subproblems by setting 
(t + -9.25) equal to 5.963430221 and -5.963430221.

Subproblem 1

t + -9.25 = 5.963430221 Simplifying t + -9.25 = 5.963430221 Reorder the terms: -9.25 + t = 5.963430221 Solving -9.25 + t = 5.963430221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + t = 5.963430221 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + t = 5.963430221 + 9.25 t = 5.963430221 + 9.25 Combine like terms: 5.963430221 + 9.25 = 15.213430221 t = 15.213430221 Simplifying t = 15.213430221

Subproblem 2

t + -9.25 = -5.963430221 Simplifying t + -9.25 = -5.963430221 Reorder the terms: -9.25 + t = -5.963430221 Solving -9.25 + t = -5.963430221 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '9.25' to each side of the equation. -9.25 + 9.25 + t = -5.963430221 + 9.25 Combine like terms: -9.25 + 9.25 = 0.00 0.00 + t = -5.963430221 + 9.25 t = -5.963430221 + 9.25 Combine like terms: -5.963430221 + 9.25 = 3.286569779 t = 3.286569779 Simplifying t = 3.286569779

Solution

The solution to the problem is based on the solutions from the subproblems. t = {15.213430221, 3.286569779}

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