x^2-80x-5000=0

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Solution for x^2-80x-5000=0 equation:


Simplifying
x2 + -80x + -5000 = 0

Reorder the terms:
-5000 + -80x + x2 = 0

Solving
-5000 + -80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '5000' to each side of the equation.
-5000 + -80x + 5000 + x2 = 0 + 5000

Reorder the terms:
-5000 + 5000 + -80x + x2 = 0 + 5000

Combine like terms: -5000 + 5000 = 0
0 + -80x + x2 = 0 + 5000
-80x + x2 = 0 + 5000

Combine like terms: 0 + 5000 = 5000
-80x + x2 = 5000

The x term is -80x.  Take half its coefficient (-40).
Square it (1600) and add it to both sides.

Add '1600' to each side of the equation.
-80x + 1600 + x2 = 5000 + 1600

Reorder the terms:
1600 + -80x + x2 = 5000 + 1600

Combine like terms: 5000 + 1600 = 6600
1600 + -80x + x2 = 6600

Factor a perfect square on the left side:
(x + -40)(x + -40) = 6600

Calculate the square root of the right side: 81.240384046

Break this problem into two subproblems by setting 
(x + -40) equal to 81.240384046 and -81.240384046.

Subproblem 1

x + -40 = 81.240384046 Simplifying x + -40 = 81.240384046 Reorder the terms: -40 + x = 81.240384046 Solving -40 + x = 81.240384046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = 81.240384046 + 40 Combine like terms: -40 + 40 = 0 0 + x = 81.240384046 + 40 x = 81.240384046 + 40 Combine like terms: 81.240384046 + 40 = 121.240384046 x = 121.240384046 Simplifying x = 121.240384046

Subproblem 2

x + -40 = -81.240384046 Simplifying x + -40 = -81.240384046 Reorder the terms: -40 + x = -81.240384046 Solving -40 + x = -81.240384046 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + x = -81.240384046 + 40 Combine like terms: -40 + 40 = 0 0 + x = -81.240384046 + 40 x = -81.240384046 + 40 Combine like terms: -81.240384046 + 40 = -41.240384046 x = -41.240384046 Simplifying x = -41.240384046

Solution

The solution to the problem is based on the solutions from the subproblems. x = {121.240384046, -41.240384046}

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