x^2+10x-190=0

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Solution for x^2+10x-190=0 equation: 


Simplifying
x2 + 10x + -190 = 0

Reorder the terms:
-190 + 10x + x2 = 0

Solving
-190 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '190' to each side of the equation.
-190 + 10x + 190 + x2 = 0 + 190

Reorder the terms:
-190 + 190 + 10x + x2 = 0 + 190

Combine like terms: -190 + 190 = 0
0 + 10x + x2 = 0 + 190
10x + x2 = 0 + 190

Combine like terms: 0 + 190 = 190
10x + x2 = 190

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 = 190 + 25

Reorder the terms:
25 + 10x + x2 = 190 + 25

Combine like terms: 190 + 25 = 215
25 + 10x + x2 = 215

Factor a perfect square on the left side:
(x + 5)(x + 5) = 215

Calculate the square root of the right side: 14.662878299

Break this problem into two subproblems by setting 
(x + 5) equal to 14.662878299 and -14.662878299.


Subproblem 1
x + 5 = 14.662878299

Simplifying
x + 5 = 14.662878299

Reorder the terms:
5 + x = 14.662878299

Solving
5 + x = 14.662878299

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 = 14.662878299 + -5

Combine like terms: 5 + -5 = 0
0 + x = 14.662878299 + -5
x = 14.662878299 + -5

Combine like terms: 14.662878299 + -5 = 9.662878299
x = 9.662878299

Simplifying
x = 9.662878299


Subproblem 2
x + 5 = -14.662878299

Simplifying
x + 5 = -14.662878299

Reorder the terms:
5 + x = -14.662878299

Solving
5 + x = -14.662878299

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 = -14.662878299 + -5

Combine like terms: 5 + -5 = 0
0 + x = -14.662878299 + -5
x = -14.662878299 + -5

Combine like terms: -14.662878299 + -5 = -19.662878299
x = -19.662878299

Simplifying
x = -19.662878299


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.662878299, -19.662878299}

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