200=2t^2-8t+5

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Solution for 200=2t^2-8t+5 equation:


Simplifying
200 = 2t2 + -8t + 5

Reorder the terms:
200 = 5 + -8t + 2t2

Solving
200 = 5 + -8t + 2t2

Solving for variable 't'.

Combine like terms: 200 + -5 = 195
195 + 8t + -2t2 = 5 + -8t + 2t2 + -5 + 8t + -2t2

Reorder the terms:
195 + 8t + -2t2 = 5 + -5 + -8t + 8t + 2t2 + -2t2

Combine like terms: 5 + -5 = 0
195 + 8t + -2t2 = 0 + -8t + 8t + 2t2 + -2t2
195 + 8t + -2t2 = -8t + 8t + 2t2 + -2t2

Combine like terms: -8t + 8t = 0
195 + 8t + -2t2 = 0 + 2t2 + -2t2
195 + 8t + -2t2 = 2t2 + -2t2

Combine like terms: 2t2 + -2t2 = 0
195 + 8t + -2t2 = 0

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

Divide each side by '-2'.
-97.5 + -4t + t2 = 0

Move the constant term to the right:

Add '97.5' to each side of the equation.
-97.5 + -4t + 97.5 + t2 = 0 + 97.5

Reorder the terms:
-97.5 + 97.5 + -4t + t2 = 0 + 97.5

Combine like terms: -97.5 + 97.5 = 0.0
0.0 + -4t + t2 = 0 + 97.5
-4t + t2 = 0 + 97.5

Combine like terms: 0 + 97.5 = 97.5
-4t + t2 = 97.5

The t term is -4t.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4t + 4 + t2 = 97.5 + 4

Reorder the terms:
4 + -4t + t2 = 97.5 + 4

Combine like terms: 97.5 + 4 = 101.5
4 + -4t + t2 = 101.5

Factor a perfect square on the left side:
(t + -2)(t + -2) = 101.5

Calculate the square root of the right side: 10.07472084

Break this problem into two subproblems by setting 
(t + -2) equal to 10.07472084 and -10.07472084.

Subproblem 1

t + -2 = 10.07472084 Simplifying t + -2 = 10.07472084 Reorder the terms: -2 + t = 10.07472084 Solving -2 + t = 10.07472084 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 10.07472084 + 2 Combine like terms: -2 + 2 = 0 0 + t = 10.07472084 + 2 t = 10.07472084 + 2 Combine like terms: 10.07472084 + 2 = 12.07472084 t = 12.07472084 Simplifying t = 12.07472084

Subproblem 2

t + -2 = -10.07472084 Simplifying t + -2 = -10.07472084 Reorder the terms: -2 + t = -10.07472084 Solving -2 + t = -10.07472084 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -10.07472084 + 2 Combine like terms: -2 + 2 = 0 0 + t = -10.07472084 + 2 t = -10.07472084 + 2 Combine like terms: -10.07472084 + 2 = -8.07472084 t = -8.07472084 Simplifying t = -8.07472084

Solution

The solution to the problem is based on the solutions from the subproblems. t = {12.07472084, -8.07472084}

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