19.884t^2-107.22t+125.56=0

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Solution for 19.884t^2-107.22t+125.56=0 equation:


Simplifying
19.884t2 + -107.22t + 125.56 = 0

Reorder the terms:
125.56 + -107.22t + 19.884t2 = 0

Solving
125.56 + -107.22t + 19.884t2 = 0

Solving for variable 't'.

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

Divide each side by '19.884'.
6.314624824 + -5.392275196t + t2 = 0

Move the constant term to the right:

Add '-6.314624824' to each side of the equation.
6.314624824 + -5.392275196t + -6.314624824 + t2 = 0 + -6.314624824

Reorder the terms:
6.314624824 + -6.314624824 + -5.392275196t + t2 = 0 + -6.314624824

Combine like terms: 6.314624824 + -6.314624824 = 0.000000000
0.000000000 + -5.392275196t + t2 = 0 + -6.314624824
-5.392275196t + t2 = 0 + -6.314624824

Combine like terms: 0 + -6.314624824 = -6.314624824
-5.392275196t + t2 = -6.314624824

The t term is -5.392275196t.  Take half its coefficient (-2.696137598).
Square it (7.269157947) and add it to both sides.

Add '7.269157947' to each side of the equation.
-5.392275196t + 7.269157947 + t2 = -6.314624824 + 7.269157947

Reorder the terms:
7.269157947 + -5.392275196t + t2 = -6.314624824 + 7.269157947

Combine like terms: -6.314624824 + 7.269157947 = 0.954533123
7.269157947 + -5.392275196t + t2 = 0.954533123

Factor a perfect square on the left side:
(t + -2.696137598)(t + -2.696137598) = 0.954533123

Calculate the square root of the right side: 0.97700211

Break this problem into two subproblems by setting 
(t + -2.696137598) equal to 0.97700211 and -0.97700211.

Subproblem 1

t + -2.696137598 = 0.97700211 Simplifying t + -2.696137598 = 0.97700211 Reorder the terms: -2.696137598 + t = 0.97700211 Solving -2.696137598 + t = 0.97700211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.696137598' to each side of the equation. -2.696137598 + 2.696137598 + t = 0.97700211 + 2.696137598 Combine like terms: -2.696137598 + 2.696137598 = 0.000000000 0.000000000 + t = 0.97700211 + 2.696137598 t = 0.97700211 + 2.696137598 Combine like terms: 0.97700211 + 2.696137598 = 3.673139708 t = 3.673139708 Simplifying t = 3.673139708

Subproblem 2

t + -2.696137598 = -0.97700211 Simplifying t + -2.696137598 = -0.97700211 Reorder the terms: -2.696137598 + t = -0.97700211 Solving -2.696137598 + t = -0.97700211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.696137598' to each side of the equation. -2.696137598 + 2.696137598 + t = -0.97700211 + 2.696137598 Combine like terms: -2.696137598 + 2.696137598 = 0.000000000 0.000000000 + t = -0.97700211 + 2.696137598 t = -0.97700211 + 2.696137598 Combine like terms: -0.97700211 + 2.696137598 = 1.719135488 t = 1.719135488 Simplifying t = 1.719135488

Solution

The solution to the problem is based on the solutions from the subproblems. t = {3.673139708, 1.719135488}

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