2x(x+7)=-5

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


Simplifying
2x(x + 7) = -5

Reorder the terms:
2x(7 + x) = -5
(7 * 2x + x * 2x) = -5
(14x + 2x2) = -5

Solving
14x + 2x2 = -5

Solving for variable 'x'.

Reorder the terms:
5 + 14x + 2x2 = -5 + 5

Combine like terms: -5 + 5 = 0
5 + 14x + 2x2 = 0

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

Divide each side by '2'.
2.5 + 7x + x2 = 0

Move the constant term to the right:

Add '-2.5' to each side of the equation.
2.5 + 7x + -2.5 + x2 = 0 + -2.5

Reorder the terms:
2.5 + -2.5 + 7x + x2 = 0 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + 7x + x2 = 0 + -2.5
7x + x2 = 0 + -2.5

Combine like terms: 0 + -2.5 = -2.5
7x + x2 = -2.5

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = -2.5 + 12.25

Reorder the terms:
12.25 + 7x + x2 = -2.5 + 12.25

Combine like terms: -2.5 + 12.25 = 9.75
12.25 + 7x + x2 = 9.75

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 9.75

Calculate the square root of the right side: 3.122498999

Break this problem into two subproblems by setting 
(x + 3.5) equal to 3.122498999 and -3.122498999.


Subproblem 1
x + 3.5 = 3.122498999

Simplifying
x + 3.5 = 3.122498999

Reorder the terms:
3.5 + x = 3.122498999

Solving
3.5 + x = 3.122498999

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 3.122498999 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 3.122498999 + -3.5
x = 3.122498999 + -3.5

Combine like terms: 3.122498999 + -3.5 = -0.377501001
x = -0.377501001

Simplifying
x = -0.377501001


Subproblem 2
x + 3.5 = -3.122498999

Simplifying
x + 3.5 = -3.122498999

Reorder the terms:
3.5 + x = -3.122498999

Solving
3.5 + x = -3.122498999

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -3.122498999 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -3.122498999 + -3.5
x = -3.122498999 + -3.5

Combine like terms: -3.122498999 + -3.5 = -6.622498999
x = -6.622498999

Simplifying
x = -6.622498999


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.377501001, -6.622498999}

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