x^2-110x-1360=0

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Solution for x^2-110x-1360=0 equation:


Simplifying
x2 + -110x + -1360 = 0

Reorder the terms:
-1360 + -110x + x2 = 0

Solving
-1360 + -110x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1360' to each side of the equation.
-1360 + -110x + 1360 + x2 = 0 + 1360

Reorder the terms:
-1360 + 1360 + -110x + x2 = 0 + 1360

Combine like terms: -1360 + 1360 = 0
0 + -110x + x2 = 0 + 1360
-110x + x2 = 0 + 1360

Combine like terms: 0 + 1360 = 1360
-110x + x2 = 1360

The x term is -110x.  Take half its coefficient (-55).
Square it (3025) and add it to both sides.

Add '3025' to each side of the equation.
-110x + 3025 + x2 = 1360 + 3025

Reorder the terms:
3025 + -110x + x2 = 1360 + 3025

Combine like terms: 1360 + 3025 = 4385
3025 + -110x + x2 = 4385

Factor a perfect square on the left side:
(x + -55)(x + -55) = 4385

Calculate the square root of the right side: 66.219332525

Break this problem into two subproblems by setting 
(x + -55) equal to 66.219332525 and -66.219332525.

Subproblem 1

x + -55 = 66.219332525 Simplifying x + -55 = 66.219332525 Reorder the terms: -55 + x = 66.219332525 Solving -55 + x = 66.219332525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = 66.219332525 + 55 Combine like terms: -55 + 55 = 0 0 + x = 66.219332525 + 55 x = 66.219332525 + 55 Combine like terms: 66.219332525 + 55 = 121.219332525 x = 121.219332525 Simplifying x = 121.219332525

Subproblem 2

x + -55 = -66.219332525 Simplifying x + -55 = -66.219332525 Reorder the terms: -55 + x = -66.219332525 Solving -55 + x = -66.219332525 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '55' to each side of the equation. -55 + 55 + x = -66.219332525 + 55 Combine like terms: -55 + 55 = 0 0 + x = -66.219332525 + 55 x = -66.219332525 + 55 Combine like terms: -66.219332525 + 55 = -11.219332525 x = -11.219332525 Simplifying x = -11.219332525

Solution

The solution to the problem is based on the solutions from the subproblems. x = {121.219332525, -11.219332525}

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