x^2-10x-488=0

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Solution for x^2-10x-488=0 equation: 


Simplifying
x2 + -10x + -488 = 0

Reorder the terms:
-488 + -10x + x2 = 0

Solving
-488 + -10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '488' to each side of the equation.
-488 + -10x + 488 + x2 = 0 + 488

Reorder the terms:
-488 + 488 + -10x + x2 = 0 + 488

Combine like terms: -488 + 488 = 0
0 + -10x + x2 = 0 + 488
-10x + x2 = 0 + 488

Combine like terms: 0 + 488 = 488
-10x + x2 = 488

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 488 + 25

Reorder the terms:
25 + -10x + x2 = 488 + 25

Combine like terms: 488 + 25 = 513
25 + -10x + x2 = 513

Factor a perfect square on the left side:
(x + -5)(x + -5) = 513

Calculate the square root of the right side: 22.649503306

Break this problem into two subproblems by setting 
(x + -5) equal to 22.649503306 and -22.649503306.


Subproblem 1
x + -5 = 22.649503306

Simplifying
x + -5 = 22.649503306

Reorder the terms:
-5 + x = 22.649503306

Solving
-5 + x = 22.649503306

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = 22.649503306 + 5

Combine like terms: -5 + 5 = 0
0 + x = 22.649503306 + 5
x = 22.649503306 + 5

Combine like terms: 22.649503306 + 5 = 27.649503306
x = 27.649503306

Simplifying
x = 27.649503306


Subproblem 2
x + -5 = -22.649503306

Simplifying
x + -5 = -22.649503306

Reorder the terms:
-5 + x = -22.649503306

Solving
-5 + x = -22.649503306

Solving for variable 'x'.

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

Add '5' to each side of the equation.
-5 + 5 + x = -22.649503306 + 5

Combine like terms: -5 + 5 = 0
0 + x = -22.649503306 + 5
x = -22.649503306 + 5

Combine like terms: -22.649503306 + 5 = -17.649503306
x = -17.649503306

Simplifying
x = -17.649503306


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {27.649503306, -17.649503306}

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