x^2+14x=0.009

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Solution for x^2+14x=0.009 equation: 


Simplifying
x2 + 14x = 0.009

Reorder the terms:
14x + x2 = 0.009

Solving
14x + x2 = 0.009

Solving for variable 'x'.

Reorder the terms:
-0.009 + 14x + x2 = 0.009 + -0.009

Combine like terms: 0.009 + -0.009 = 0.000
-0.009 + 14x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.009' to each side of the equation.
-0.009 + 14x + 0.009 + x2 = 0.000 + 0.009

Reorder the terms:
-0.009 + 0.009 + 14x + x2 = 0.000 + 0.009

Combine like terms: -0.009 + 0.009 = 0.000
0.000 + 14x + x2 = 0.000 + 0.009
14x + x2 = 0.000 + 0.009

Combine like terms: 0.000 + 0.009 = 0.009
14x + x2 = 0.009

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = 0.009 + 49

Reorder the terms:
49 + 14x + x2 = 0.009 + 49

Combine like terms: 0.009 + 49 = 49.009
49 + 14x + x2 = 49.009

Factor a perfect square on the left side:
(x + 7)(x + 7) = 49.009

Calculate the square root of the right side: 7.000642828

Break this problem into two subproblems by setting 
(x + 7) equal to 7.000642828 and -7.000642828.


Subproblem 1
x + 7 = 7.000642828

Simplifying
x + 7 = 7.000642828

Reorder the terms:
7 + x = 7.000642828

Solving
7 + x = 7.000642828

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 7.000642828 + -7

Combine like terms: 7 + -7 = 0
0 + x = 7.000642828 + -7
x = 7.000642828 + -7

Combine like terms: 7.000642828 + -7 = 0.000642828
x = 0.000642828

Simplifying
x = 0.000642828


Subproblem 2
x + 7 = -7.000642828

Simplifying
x + 7 = -7.000642828

Reorder the terms:
7 + x = -7.000642828

Solving
7 + x = -7.000642828

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -7.000642828 + -7

Combine like terms: 7 + -7 = 0
0 + x = -7.000642828 + -7
x = -7.000642828 + -7

Combine like terms: -7.000642828 + -7 = -14.000642828
x = -14.000642828

Simplifying
x = -14.000642828


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.000642828, -14.000642828}

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