X^2+0.0007X-0.007=0

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Solution for X^2+0.0007X-0.007=0 equation: 


Simplifying
X2 + 0.0007X + -0.007 = 0

Reorder the terms:
-0.007 + 0.0007X + X2 = 0

Solving
-0.007 + 0.0007X + X2 = 0

Solving for variable 'X'.

Begin completing the square.

Move the constant term to the right:

Add '0.007' to each side of the equation.
-0.007 + 0.0007X + 0.007 + X2 = 0 + 0.007

Reorder the terms:
-0.007 + 0.007 + 0.0007X + X2 = 0 + 0.007

Combine like terms: -0.007 + 0.007 = 0.000
0.000 + 0.0007X + X2 = 0 + 0.007
0.0007X + X2 = 0 + 0.007

Combine like terms: 0 + 0.007 = 0.007
0.0007X + X2 = 0.007

The X term is 0.0007X.  Take half its coefficient (0.00035).
Square it (0.0000001225) and add it to both sides.

Add '0.0000001225' to each side of the equation.
0.0007X + 0.0000001225 + X2 = 0.007 + 0.0000001225

Reorder the terms:
0.0000001225 + 0.0007X + X2 = 0.007 + 0.0000001225

Combine like terms: 0.007 + 0.0000001225 = 0.0070001225
0.0000001225 + 0.0007X + X2 = 0.0070001225

Factor a perfect square on the left side:
(X + 0.00035)(X + 0.00035) = 0.0070001225

Calculate the square root of the right side: 0.083666735

Break this problem into two subproblems by setting 
(X + 0.00035) equal to 0.083666735 and -0.083666735.


Subproblem 1
X + 0.00035 = 0.083666735

Simplifying
X + 0.00035 = 0.083666735

Reorder the terms:
0.00035 + X = 0.083666735

Solving
0.00035 + X = 0.083666735

Solving for variable 'X'.

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

Add '-0.00035' to each side of the equation.
0.00035 + -0.00035 + X = 0.083666735 + -0.00035

Combine like terms: 0.00035 + -0.00035 = 0.00000
0.00000 + X = 0.083666735 + -0.00035
X = 0.083666735 + -0.00035

Combine like terms: 0.083666735 + -0.00035 = 0.083316735
X = 0.083316735

Simplifying
X = 0.083316735


Subproblem 2
X + 0.00035 = -0.083666735

Simplifying
X + 0.00035 = -0.083666735

Reorder the terms:
0.00035 + X = -0.083666735

Solving
0.00035 + X = -0.083666735

Solving for variable 'X'.

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

Add '-0.00035' to each side of the equation.
0.00035 + -0.00035 + X = -0.083666735 + -0.00035

Combine like terms: 0.00035 + -0.00035 = 0.00000
0.00000 + X = -0.083666735 + -0.00035
X = -0.083666735 + -0.00035

Combine like terms: -0.083666735 + -0.00035 = -0.084016735
X = -0.084016735

Simplifying
X = -0.084016735


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.083316735, -0.084016735}

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