x^2-x-2880=0

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Solution for x^2-x-2880=0 equation:


Simplifying
x2 + -1x + -2880 = 0

Reorder the terms:
-2880 + -1x + x2 = 0

Solving
-2880 + -1x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '2880' to each side of the equation.
-2880 + -1x + 2880 + x2 = 0 + 2880

Reorder the terms:
-2880 + 2880 + -1x + x2 = 0 + 2880

Combine like terms: -2880 + 2880 = 0
0 + -1x + x2 = 0 + 2880
-1x + x2 = 0 + 2880

Combine like terms: 0 + 2880 = 2880
-1x + x2 = 2880

The x term is -1x.  Take half its coefficient (-0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
-1x + 0.25 + x2 = 2880 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 2880 + 0.25

Combine like terms: 2880 + 0.25 = 2880.25
0.25 + -1x + x2 = 2880.25

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 2880.25

Calculate the square root of the right side: 53.667960647

Break this problem into two subproblems by setting 
(x + -0.5) equal to 53.667960647 and -53.667960647.

Subproblem 1

x + -0.5 = 53.667960647 Simplifying x + -0.5 = 53.667960647 Reorder the terms: -0.5 + x = 53.667960647 Solving -0.5 + x = 53.667960647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 53.667960647 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 53.667960647 + 0.5 x = 53.667960647 + 0.5 Combine like terms: 53.667960647 + 0.5 = 54.167960647 x = 54.167960647 Simplifying x = 54.167960647

Subproblem 2

x + -0.5 = -53.667960647 Simplifying x + -0.5 = -53.667960647 Reorder the terms: -0.5 + x = -53.667960647 Solving -0.5 + x = -53.667960647 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -53.667960647 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -53.667960647 + 0.5 x = -53.667960647 + 0.5 Combine like terms: -53.667960647 + 0.5 = -53.167960647 x = -53.167960647 Simplifying x = -53.167960647

Solution

The solution to the problem is based on the solutions from the subproblems. x = {54.167960647, -53.167960647}

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