x^2-43x+340=0

Solution for x^2-43x+340=0 equation:

Simplifying
x2 + -43x + 340 = 0

Reorder the terms:
340 + -43x + x2 = 0

Solving
340 + -43x + 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 + -43x + -340 + x2 = 0 + -340

Reorder the terms:
340 + -340 + -43x + x2 = 0 + -340

Combine like terms: 340 + -340 = 0
0 + -43x + x2 = 0 + -340
-43x + x2 = 0 + -340

Combine like terms: 0 + -340 = -340
-43x + x2 = -340

The x term is -43x.  Take half its coefficient (-21.5).
Square it (462.25) and add it to both sides.

Add '462.25' to each side of the equation.
-43x + 462.25 + x2 = -340 + 462.25

Reorder the terms:
462.25 + -43x + x2 = -340 + 462.25

Combine like terms: -340 + 462.25 = 122.25
462.25 + -43x + x2 = 122.25

Factor a perfect square on the left side:
(x + -21.5)(x + -21.5) = 122.25

Calculate the square root of the right side: 11.056672194

Break this problem into two subproblems by setting 
(x + -21.5) equal to 11.056672194 and -11.056672194.

Subproblem 1
x + -21.5 = 11.056672194

Simplifying
x + -21.5 = 11.056672194

Reorder the terms:
-21.5 + x = 11.056672194

Solving
-21.5 + x = 11.056672194

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '21.5' to each side of the equation.
-21.5 + 21.5 + x = 11.056672194 + 21.5

Combine like terms: -21.5 + 21.5 = 0.0
0.0 + x = 11.056672194 + 21.5
x = 11.056672194 + 21.5

Combine like terms: 11.056672194 + 21.5 = 32.556672194
x = 32.556672194

Simplifying
x = 32.556672194

Subproblem 2
x + -21.5 = -11.056672194

Simplifying
x + -21.5 = -11.056672194

Reorder the terms:
-21.5 + x = -11.056672194

Solving
-21.5 + x = -11.056672194

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '21.5' to each side of the equation.
-21.5 + 21.5 + x = -11.056672194 + 21.5

Combine like terms: -21.5 + 21.5 = 0.0
0.0 + x = -11.056672194 + 21.5
x = -11.056672194 + 21.5

Combine like terms: -11.056672194 + 21.5 = 10.443327806
x = 10.443327806

Simplifying
x = 10.443327806

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {32.556672194, 10.443327806}