33.57=2.2t+0.865t^2

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Solution for 33.57=2.2t+0.865t^2 equation:


Simplifying
33.57 = 2.2t + 0.865t2

Solving
33.57 = 2.2t + 0.865t2

Solving for variable 't'.

Reorder the terms:
33.57 + -2.2t + -0.865t2 = 2.2t + -2.2t + 0.865t2 + -0.865t2

Combine like terms: 2.2t + -2.2t = 0.0
33.57 + -2.2t + -0.865t2 = 0.0 + 0.865t2 + -0.865t2
33.57 + -2.2t + -0.865t2 = 0.865t2 + -0.865t2

Combine like terms: 0.865t2 + -0.865t2 = 0.000
33.57 + -2.2t + -0.865t2 = 0.000

Begin completing the square.  Divide all terms by
-0.865 the coefficient of the squared term: 

Divide each side by '-0.865'.
-38.80924855 + 2.543352601t + t2 = 0

Move the constant term to the right:

Add '38.80924855' to each side of the equation.
-38.80924855 + 2.543352601t + 38.80924855 + t2 = 0 + 38.80924855

Reorder the terms:
-38.80924855 + 38.80924855 + 2.543352601t + t2 = 0 + 38.80924855

Combine like terms: -38.80924855 + 38.80924855 = 0.00000000
0.00000000 + 2.543352601t + t2 = 0 + 38.80924855
2.543352601t + t2 = 0 + 38.80924855

Combine like terms: 0 + 38.80924855 = 38.80924855
2.543352601t + t2 = 38.80924855

The t term is 2.543352601t.  Take half its coefficient (1.271676301).
Square it (1.617160615) and add it to both sides.

Add '1.617160615' to each side of the equation.
2.543352601t + 1.617160615 + t2 = 38.80924855 + 1.617160615

Reorder the terms:
1.617160615 + 2.543352601t + t2 = 38.80924855 + 1.617160615

Combine like terms: 38.80924855 + 1.617160615 = 40.426409165
1.617160615 + 2.543352601t + t2 = 40.426409165

Factor a perfect square on the left side:
(t + 1.271676301)(t + 1.271676301) = 40.426409165

Calculate the square root of the right side: 6.35817656

Break this problem into two subproblems by setting 
(t + 1.271676301) equal to 6.35817656 and -6.35817656.

Subproblem 1

t + 1.271676301 = 6.35817656 Simplifying t + 1.271676301 = 6.35817656 Reorder the terms: 1.271676301 + t = 6.35817656 Solving 1.271676301 + t = 6.35817656 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.271676301' to each side of the equation. 1.271676301 + -1.271676301 + t = 6.35817656 + -1.271676301 Combine like terms: 1.271676301 + -1.271676301 = 0.000000000 0.000000000 + t = 6.35817656 + -1.271676301 t = 6.35817656 + -1.271676301 Combine like terms: 6.35817656 + -1.271676301 = 5.086500259 t = 5.086500259 Simplifying t = 5.086500259

Subproblem 2

t + 1.271676301 = -6.35817656 Simplifying t + 1.271676301 = -6.35817656 Reorder the terms: 1.271676301 + t = -6.35817656 Solving 1.271676301 + t = -6.35817656 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.271676301' to each side of the equation. 1.271676301 + -1.271676301 + t = -6.35817656 + -1.271676301 Combine like terms: 1.271676301 + -1.271676301 = 0.000000000 0.000000000 + t = -6.35817656 + -1.271676301 t = -6.35817656 + -1.271676301 Combine like terms: -6.35817656 + -1.271676301 = -7.629852861 t = -7.629852861 Simplifying t = -7.629852861

Solution

The solution to the problem is based on the solutions from the subproblems. t = {5.086500259, -7.629852861}

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