x^2-4x-43=0

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Solution for x^2-4x-43=0 equation: 


Simplifying
x2 + -4x + -43 = 0

Reorder the terms:
-43 + -4x + x2 = 0

Solving
-43 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + -4x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + -4x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + -4x + x2 = 0 + 43
-4x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
-4x + x2 = 43

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 43 + 4

Reorder the terms:
4 + -4x + x2 = 43 + 4

Combine like terms: 43 + 4 = 47
4 + -4x + x2 = 47

Factor a perfect square on the left side:
(x + -2)(x + -2) = 47

Calculate the square root of the right side: 6.8556546

Break this problem into two subproblems by setting 
(x + -2) equal to 6.8556546 and -6.8556546.


Subproblem 1
x + -2 = 6.8556546

Simplifying
x + -2 = 6.8556546

Reorder the terms:
-2 + x = 6.8556546

Solving
-2 + x = 6.8556546

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 6.8556546 + 2

Combine like terms: -2 + 2 = 0
0 + x = 6.8556546 + 2
x = 6.8556546 + 2

Combine like terms: 6.8556546 + 2 = 8.8556546
x = 8.8556546

Simplifying
x = 8.8556546


Subproblem 2
x + -2 = -6.8556546

Simplifying
x + -2 = -6.8556546

Reorder the terms:
-2 + x = -6.8556546

Solving
-2 + x = -6.8556546

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -6.8556546 + 2

Combine like terms: -2 + 2 = 0
0 + x = -6.8556546 + 2
x = -6.8556546 + 2

Combine like terms: -6.8556546 + 2 = -4.8556546
x = -4.8556546

Simplifying
x = -4.8556546


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.8556546, -4.8556546}

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