x^2+10x-19=0

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Solution for x^2+10x-19=0 equation: 


Simplifying
x2 + 10x + -19 = 0

Reorder the terms:
-19 + 10x + x2 = 0

Solving
-19 + 10x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 10x + 19 + x2 = 0 + 19

Reorder the terms:
-19 + 19 + 10x + x2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 10x + x2 = 0 + 19
10x + x2 = 0 + 19

Combine like terms: 0 + 19 = 19
10x + x2 = 19

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 = 19 + 25

Reorder the terms:
25 + 10x + x2 = 19 + 25

Combine like terms: 19 + 25 = 44
25 + 10x + x2 = 44

Factor a perfect square on the left side:
(x + 5)(x + 5) = 44

Calculate the square root of the right side: 6.633249581

Break this problem into two subproblems by setting 
(x + 5) equal to 6.633249581 and -6.633249581.


Subproblem 1
x + 5 = 6.633249581

Simplifying
x + 5 = 6.633249581

Reorder the terms:
5 + x = 6.633249581

Solving
5 + x = 6.633249581

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 = 6.633249581 + -5

Combine like terms: 5 + -5 = 0
0 + x = 6.633249581 + -5
x = 6.633249581 + -5

Combine like terms: 6.633249581 + -5 = 1.633249581
x = 1.633249581

Simplifying
x = 1.633249581


Subproblem 2
x + 5 = -6.633249581

Simplifying
x + 5 = -6.633249581

Reorder the terms:
5 + x = -6.633249581

Solving
5 + x = -6.633249581

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 = -6.633249581 + -5

Combine like terms: 5 + -5 = 0
0 + x = -6.633249581 + -5
x = -6.633249581 + -5

Combine like terms: -6.633249581 + -5 = -11.633249581
x = -11.633249581

Simplifying
x = -11.633249581


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.633249581, -11.633249581}

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