2t^2-55t-350=0

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Solution for 2t^2-55t-350=0 equation:


Simplifying
2t2 + -55t + -350 = 0

Reorder the terms:
-350 + -55t + 2t2 = 0

Solving
-350 + -55t + 2t2 = 0

Solving for variable 't'.

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

Divide each side by '2'.
-175 + -27.5t + t2 = 0

Move the constant term to the right:

Add '175' to each side of the equation.
-175 + -27.5t + 175 + t2 = 0 + 175

Reorder the terms:
-175 + 175 + -27.5t + t2 = 0 + 175

Combine like terms: -175 + 175 = 0
0 + -27.5t + t2 = 0 + 175
-27.5t + t2 = 0 + 175

Combine like terms: 0 + 175 = 175
-27.5t + t2 = 175

The t term is -27.5t.  Take half its coefficient (-13.75).
Square it (189.0625) and add it to both sides.

Add '189.0625' to each side of the equation.
-27.5t + 189.0625 + t2 = 175 + 189.0625

Reorder the terms:
189.0625 + -27.5t + t2 = 175 + 189.0625

Combine like terms: 175 + 189.0625 = 364.0625
189.0625 + -27.5t + t2 = 364.0625

Factor a perfect square on the left side:
(t + -13.75)(t + -13.75) = 364.0625

Calculate the square root of the right side: 19.080421903

Break this problem into two subproblems by setting 
(t + -13.75) equal to 19.080421903 and -19.080421903.

Subproblem 1

t + -13.75 = 19.080421903 Simplifying t + -13.75 = 19.080421903 Reorder the terms: -13.75 + t = 19.080421903 Solving -13.75 + t = 19.080421903 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + t = 19.080421903 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + t = 19.080421903 + 13.75 t = 19.080421903 + 13.75 Combine like terms: 19.080421903 + 13.75 = 32.830421903 t = 32.830421903 Simplifying t = 32.830421903

Subproblem 2

t + -13.75 = -19.080421903 Simplifying t + -13.75 = -19.080421903 Reorder the terms: -13.75 + t = -19.080421903 Solving -13.75 + t = -19.080421903 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '13.75' to each side of the equation. -13.75 + 13.75 + t = -19.080421903 + 13.75 Combine like terms: -13.75 + 13.75 = 0.00 0.00 + t = -19.080421903 + 13.75 t = -19.080421903 + 13.75 Combine like terms: -19.080421903 + 13.75 = -5.330421903 t = -5.330421903 Simplifying t = -5.330421903

Solution

The solution to the problem is based on the solutions from the subproblems. t = {32.830421903, -5.330421903}

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