x^2-80x-340=0

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Solution for x^2-80x-340=0 equation: 


Simplifying
x2 + -80x + -340 = 0

Reorder the terms:
-340 + -80x + x2 = 0

Solving
-340 + -80x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '340' to each side of the equation.
-340 + -80x + 340 + x2 = 0 + 340

Reorder the terms:
-340 + 340 + -80x + x2 = 0 + 340

Combine like terms: -340 + 340 = 0
0 + -80x + x2 = 0 + 340
-80x + x2 = 0 + 340

Combine like terms: 0 + 340 = 340
-80x + x2 = 340

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 = 340 + 1600

Reorder the terms:
1600 + -80x + x2 = 340 + 1600

Combine like terms: 340 + 1600 = 1940
1600 + -80x + x2 = 1940

Factor a perfect square on the left side:
(x + -40)(x + -40) = 1940

Calculate the square root of the right side: 44.045431091

Break this problem into two subproblems by setting 
(x + -40) equal to 44.045431091 and -44.045431091.


Subproblem 1
x + -40 = 44.045431091

Simplifying
x + -40 = 44.045431091

Reorder the terms:
-40 + x = 44.045431091

Solving
-40 + x = 44.045431091

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 = 44.045431091 + 40

Combine like terms: -40 + 40 = 0
0 + x = 44.045431091 + 40
x = 44.045431091 + 40

Combine like terms: 44.045431091 + 40 = 84.045431091
x = 84.045431091

Simplifying
x = 84.045431091


Subproblem 2
x + -40 = -44.045431091

Simplifying
x + -40 = -44.045431091

Reorder the terms:
-40 + x = -44.045431091

Solving
-40 + x = -44.045431091

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 = -44.045431091 + 40

Combine like terms: -40 + 40 = 0
0 + x = -44.045431091 + 40
x = -44.045431091 + 40

Combine like terms: -44.045431091 + 40 = -4.045431091
x = -4.045431091

Simplifying
x = -4.045431091


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {84.045431091, -4.045431091}

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