2x(-5x-19)=7

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Solution for 2x(-5x-19)=7 equation: 


Simplifying
2x(-5x + -19) = 7

Reorder the terms:
2x(-19 + -5x) = 7
(-19 * 2x + -5x * 2x) = 7
(-38x + -10x2) = 7

Solving
-38x + -10x2 = 7

Solving for variable 'x'.

Reorder the terms:
-7 + -38x + -10x2 = 7 + -7

Combine like terms: 7 + -7 = 0
-7 + -38x + -10x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(7 + 38x + 10x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(7 + 38x + 10x2)' equal to zero and attempt to solve:

Simplifying
7 + 38x + 10x2 = 0

Solving
7 + 38x + 10x2 = 0

Begin completing the square.  Divide all terms by
10 the coefficient of the squared term: 

Divide each side by '10'.
0.7 + 3.8x + x2 = 0.0

Move the constant term to the right:

Add '-0.7' to each side of the equation.
0.7 + 3.8x + -0.7 + x2 = 0.0 + -0.7

Reorder the terms:
0.7 + -0.7 + 3.8x + x2 = 0.0 + -0.7

Combine like terms: 0.7 + -0.7 = 0.0
0.0 + 3.8x + x2 = 0.0 + -0.7
3.8x + x2 = 0.0 + -0.7

Combine like terms: 0.0 + -0.7 = -0.7
3.8x + x2 = -0.7

The x term is 3.8x.  Take half its coefficient (1.9).
Square it (3.61) and add it to both sides.

Add '3.61' to each side of the equation.
3.8x + 3.61 + x2 = -0.7 + 3.61

Reorder the terms:
3.61 + 3.8x + x2 = -0.7 + 3.61

Combine like terms: -0.7 + 3.61 = 2.91
3.61 + 3.8x + x2 = 2.91

Factor a perfect square on the left side:
(x + 1.9)(x + 1.9) = 2.91

Calculate the square root of the right side: 1.705872211

Break this problem into two subproblems by setting 
(x + 1.9) equal to 1.705872211 and -1.705872211.


Subproblem 1
x + 1.9 = 1.705872211

Simplifying
x + 1.9 = 1.705872211

Reorder the terms:
1.9 + x = 1.705872211

Solving
1.9 + x = 1.705872211

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = 1.705872211 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = 1.705872211 + -1.9
x = 1.705872211 + -1.9

Combine like terms: 1.705872211 + -1.9 = -0.194127789
x = -0.194127789

Simplifying
x = -0.194127789


Subproblem 2
x + 1.9 = -1.705872211

Simplifying
x + 1.9 = -1.705872211

Reorder the terms:
1.9 + x = -1.705872211

Solving
1.9 + x = -1.705872211

Solving for variable 'x'.

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

Add '-1.9' to each side of the equation.
1.9 + -1.9 + x = -1.705872211 + -1.9

Combine like terms: 1.9 + -1.9 = 0.0
0.0 + x = -1.705872211 + -1.9
x = -1.705872211 + -1.9

Combine like terms: -1.705872211 + -1.9 = -3.605872211
x = -3.605872211

Simplifying
x = -3.605872211


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.194127789, -3.605872211}
Solution
x = {-0.194127789, -3.605872211}

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