t^2-2t-200=0

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Solution for t^2-2t-200=0 equation:


Simplifying
t2 + -2t + -200 = 0

Reorder the terms:
-200 + -2t + t2 = 0

Solving
-200 + -2t + t2 = 0

Solving for variable 't'.

Begin completing the square.

Move the constant term to the right:

Add '200' to each side of the equation.
-200 + -2t + 200 + t2 = 0 + 200

Reorder the terms:
-200 + 200 + -2t + t2 = 0 + 200

Combine like terms: -200 + 200 = 0
0 + -2t + t2 = 0 + 200
-2t + t2 = 0 + 200

Combine like terms: 0 + 200 = 200
-2t + t2 = 200

The t term is -2t.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2t + 1 + t2 = 200 + 1

Reorder the terms:
1 + -2t + t2 = 200 + 1

Combine like terms: 200 + 1 = 201
1 + -2t + t2 = 201

Factor a perfect square on the left side:
(t + -1)(t + -1) = 201

Calculate the square root of the right side: 14.177446879

Break this problem into two subproblems by setting 
(t + -1) equal to 14.177446879 and -14.177446879.

Subproblem 1

t + -1 = 14.177446879 Simplifying t + -1 = 14.177446879 Reorder the terms: -1 + t = 14.177446879 Solving -1 + t = 14.177446879 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = 14.177446879 + 1 Combine like terms: -1 + 1 = 0 0 + t = 14.177446879 + 1 t = 14.177446879 + 1 Combine like terms: 14.177446879 + 1 = 15.177446879 t = 15.177446879 Simplifying t = 15.177446879

Subproblem 2

t + -1 = -14.177446879 Simplifying t + -1 = -14.177446879 Reorder the terms: -1 + t = -14.177446879 Solving -1 + t = -14.177446879 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + t = -14.177446879 + 1 Combine like terms: -1 + 1 = 0 0 + t = -14.177446879 + 1 t = -14.177446879 + 1 Combine like terms: -14.177446879 + 1 = -13.177446879 t = -13.177446879 Simplifying t = -13.177446879

Solution

The solution to the problem is based on the solutions from the subproblems. t = {15.177446879, -13.177446879}

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