x^2-2x-1200=0

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Solution for x^2-2x-1200=0 equation:


Simplifying
x2 + -2x + -1200 = 0

Reorder the terms:
-1200 + -2x + x2 = 0

Solving
-1200 + -2x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1200' to each side of the equation.
-1200 + -2x + 1200 + x2 = 0 + 1200

Reorder the terms:
-1200 + 1200 + -2x + x2 = 0 + 1200

Combine like terms: -1200 + 1200 = 0
0 + -2x + x2 = 0 + 1200
-2x + x2 = 0 + 1200

Combine like terms: 0 + 1200 = 1200
-2x + x2 = 1200

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

Add '1' to each side of the equation.
-2x + 1 + x2 = 1200 + 1

Reorder the terms:
1 + -2x + x2 = 1200 + 1

Combine like terms: 1200 + 1 = 1201
1 + -2x + x2 = 1201

Factor a perfect square on the left side:
(x + -1)(x + -1) = 1201

Calculate the square root of the right side: 34.655446902

Break this problem into two subproblems by setting 
(x + -1) equal to 34.655446902 and -34.655446902.

Subproblem 1

x + -1 = 34.655446902 Simplifying x + -1 = 34.655446902 Reorder the terms: -1 + x = 34.655446902 Solving -1 + x = 34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 34.655446902 + 1 Combine like terms: -1 + 1 = 0 0 + x = 34.655446902 + 1 x = 34.655446902 + 1 Combine like terms: 34.655446902 + 1 = 35.655446902 x = 35.655446902 Simplifying x = 35.655446902

Subproblem 2

x + -1 = -34.655446902 Simplifying x + -1 = -34.655446902 Reorder the terms: -1 + x = -34.655446902 Solving -1 + x = -34.655446902 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -34.655446902 + 1 Combine like terms: -1 + 1 = 0 0 + x = -34.655446902 + 1 x = -34.655446902 + 1 Combine like terms: -34.655446902 + 1 = -33.655446902 x = -33.655446902 Simplifying x = -33.655446902

Solution

The solution to the problem is based on the solutions from the subproblems. x = {35.655446902, -33.655446902}

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