X^2-10X-40=0

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Solution for X^2-10X-40=0 equation: 


Simplifying
X2 + -10X + -40 = 0

Reorder the terms:
-40 + -10X + X2 = 0

Solving
-40 + -10X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '40' to each side of the equation.
-40 + -10X + 40 + X2 = 0 + 40

Reorder the terms:
-40 + 40 + -10X + X2 = 0 + 40

Combine like terms: -40 + 40 = 0
0 + -10X + X2 = 0 + 40
-10X + X2 = 0 + 40

Combine like terms: 0 + 40 = 40
-10X + X2 = 40

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 = 40 + 25

Reorder the terms:
25 + -10X + X2 = 40 + 25

Combine like terms: 40 + 25 = 65
25 + -10X + X2 = 65

Factor a perfect square on the left side:
(X + -5)(X + -5) = 65

Calculate the square root of the right side: 8.062257748

Break this problem into two subproblems by setting 
(X + -5) equal to 8.062257748 and -8.062257748.


Subproblem 1
X + -5 = 8.062257748

Simplifying
X + -5 = 8.062257748

Reorder the terms:
-5 + X = 8.062257748

Solving
-5 + X = 8.062257748

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 = 8.062257748 + 5

Combine like terms: -5 + 5 = 0
0 + X = 8.062257748 + 5
X = 8.062257748 + 5

Combine like terms: 8.062257748 + 5 = 13.062257748
X = 13.062257748

Simplifying
X = 13.062257748


Subproblem 2
X + -5 = -8.062257748

Simplifying
X + -5 = -8.062257748

Reorder the terms:
-5 + X = -8.062257748

Solving
-5 + X = -8.062257748

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 = -8.062257748 + 5

Combine like terms: -5 + 5 = 0
0 + X = -8.062257748 + 5
X = -8.062257748 + 5

Combine like terms: -8.062257748 + 5 = -3.062257748
X = -3.062257748

Simplifying
X = -3.062257748


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {13.062257748, -3.062257748}

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