-x^2+64x-43=0

Solution for -x^2+64x-43=0 equation:

Simplifying
-1x2 + 64x + -43 = 0

Reorder the terms:
-43 + 64x + -1x2 = 0

Solving
-43 + 64x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
43 + -64x + x2 = 0

Move the constant term to the right:

Add '-43' to each side of the equation.
43 + -64x + -43 + x2 = 0 + -43

Reorder the terms:
43 + -43 + -64x + x2 = 0 + -43

Combine like terms: 43 + -43 = 0
0 + -64x + x2 = 0 + -43
-64x + x2 = 0 + -43

Combine like terms: 0 + -43 = -43
-64x + x2 = -43

The x term is -64x.  Take half its coefficient (-32).
Square it (1024) and add it to both sides.

Add '1024' to each side of the equation.
-64x + 1024 + x2 = -43 + 1024

Reorder the terms:
1024 + -64x + x2 = -43 + 1024

Combine like terms: -43 + 1024 = 981
1024 + -64x + x2 = 981

Factor a perfect square on the left side:
(x + -32)(x + -32) = 981

Calculate the square root of the right side: 31.320919527

Break this problem into two subproblems by setting 
(x + -32) equal to 31.320919527 and -31.320919527.

Subproblem 1
x + -32 = 31.320919527

Simplifying
x + -32 = 31.320919527

Reorder the terms:
-32 + x = 31.320919527

Solving
-32 + x = 31.320919527

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + x = 31.320919527 + 32

Combine like terms: -32 + 32 = 0
0 + x = 31.320919527 + 32
x = 31.320919527 + 32

Combine like terms: 31.320919527 + 32 = 63.320919527
x = 63.320919527

Simplifying
x = 63.320919527

Subproblem 2
x + -32 = -31.320919527

Simplifying
x + -32 = -31.320919527

Reorder the terms:
-32 + x = -31.320919527

Solving
-32 + x = -31.320919527

Solving for variable 'x'.

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

Add '32' to each side of the equation.
-32 + 32 + x = -31.320919527 + 32

Combine like terms: -32 + 32 = 0
0 + x = -31.320919527 + 32
x = -31.320919527 + 32

Combine like terms: -31.320919527 + 32 = 0.679080473
x = 0.679080473

Simplifying
x = 0.679080473

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {63.320919527, 0.679080473}