x^2-4x-287=0

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Solution for x^2-4x-287=0 equation: 


Simplifying
x2 + -4x + -287 = 0

Reorder the terms:
-287 + -4x + x2 = 0

Solving
-287 + -4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '287' to each side of the equation.
-287 + -4x + 287 + x2 = 0 + 287

Reorder the terms:
-287 + 287 + -4x + x2 = 0 + 287

Combine like terms: -287 + 287 = 0
0 + -4x + x2 = 0 + 287
-4x + x2 = 0 + 287

Combine like terms: 0 + 287 = 287
-4x + x2 = 287

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 = 287 + 4

Reorder the terms:
4 + -4x + x2 = 287 + 4

Combine like terms: 287 + 4 = 291
4 + -4x + x2 = 291

Factor a perfect square on the left side:
(x + -2)(x + -2) = 291

Calculate the square root of the right side: 17.058722109

Break this problem into two subproblems by setting 
(x + -2) equal to 17.058722109 and -17.058722109.


Subproblem 1
x + -2 = 17.058722109

Simplifying
x + -2 = 17.058722109

Reorder the terms:
-2 + x = 17.058722109

Solving
-2 + x = 17.058722109

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 = 17.058722109 + 2

Combine like terms: -2 + 2 = 0
0 + x = 17.058722109 + 2
x = 17.058722109 + 2

Combine like terms: 17.058722109 + 2 = 19.058722109
x = 19.058722109

Simplifying
x = 19.058722109


Subproblem 2
x + -2 = -17.058722109

Simplifying
x + -2 = -17.058722109

Reorder the terms:
-2 + x = -17.058722109

Solving
-2 + x = -17.058722109

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 = -17.058722109 + 2

Combine like terms: -2 + 2 = 0
0 + x = -17.058722109 + 2
x = -17.058722109 + 2

Combine like terms: -17.058722109 + 2 = -15.058722109
x = -15.058722109

Simplifying
x = -15.058722109


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.058722109, -15.058722109}

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