x^2-10x-5=15

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Solution for x^2-10x-5=15 equation: 


Simplifying
x2 + -10x + -5 = 15

Reorder the terms:
-5 + -10x + x2 = 15

Solving
-5 + -10x + x2 = 15

Solving for variable 'x'.

Reorder the terms:
-5 + -15 + -10x + x2 = 15 + -15

Combine like terms: -5 + -15 = -20
-20 + -10x + x2 = 15 + -15

Combine like terms: 15 + -15 = 0
-20 + -10x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + -10x + 20 + x2 = 0 + 20

Reorder the terms:
-20 + 20 + -10x + x2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + -10x + x2 = 0 + 20
-10x + x2 = 0 + 20

Combine like terms: 0 + 20 = 20
-10x + x2 = 20

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 = 20 + 25

Reorder the terms:
25 + -10x + x2 = 20 + 25

Combine like terms: 20 + 25 = 45
25 + -10x + x2 = 45

Factor a perfect square on the left side:
(x + -5)(x + -5) = 45

Calculate the square root of the right side: 6.708203933

Break this problem into two subproblems by setting 
(x + -5) equal to 6.708203933 and -6.708203933.


Subproblem 1
x + -5 = 6.708203933

Simplifying
x + -5 = 6.708203933

Reorder the terms:
-5 + x = 6.708203933

Solving
-5 + x = 6.708203933

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 = 6.708203933 + 5

Combine like terms: -5 + 5 = 0
0 + x = 6.708203933 + 5
x = 6.708203933 + 5

Combine like terms: 6.708203933 + 5 = 11.708203933
x = 11.708203933

Simplifying
x = 11.708203933


Subproblem 2
x + -5 = -6.708203933

Simplifying
x + -5 = -6.708203933

Reorder the terms:
-5 + x = -6.708203933

Solving
-5 + x = -6.708203933

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 = -6.708203933 + 5

Combine like terms: -5 + 5 = 0
0 + x = -6.708203933 + 5
x = -6.708203933 + 5

Combine like terms: -6.708203933 + 5 = -1.708203933
x = -1.708203933

Simplifying
x = -1.708203933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.708203933, -1.708203933}

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