x^2+.17x=.039

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Solution for x^2+.17x=.039 equation: 


Simplifying
x2 + 0.17x = 0.039

Reorder the terms:
0.17x + x2 = 0.039

Solving
0.17x + x2 = 0.039

Solving for variable 'x'.

Reorder the terms:
-0.039 + 0.17x + x2 = 0.039 + -0.039

Combine like terms: 0.039 + -0.039 = 0.000
-0.039 + 0.17x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.039' to each side of the equation.
-0.039 + 0.17x + 0.039 + x2 = 0.000 + 0.039

Reorder the terms:
-0.039 + 0.039 + 0.17x + x2 = 0.000 + 0.039

Combine like terms: -0.039 + 0.039 = 0.000
0.000 + 0.17x + x2 = 0.000 + 0.039
0.17x + x2 = 0.000 + 0.039

Combine like terms: 0.000 + 0.039 = 0.039
0.17x + x2 = 0.039

The x term is 0.17x.  Take half its coefficient (0.085).
Square it (0.007225) and add it to both sides.

Add '0.007225' to each side of the equation.
0.17x + 0.007225 + x2 = 0.039 + 0.007225

Reorder the terms:
0.007225 + 0.17x + x2 = 0.039 + 0.007225

Combine like terms: 0.039 + 0.007225 = 0.046225
0.007225 + 0.17x + x2 = 0.046225

Factor a perfect square on the left side:
(x + 0.085)(x + 0.085) = 0.046225

Calculate the square root of the right side: 0.215

Break this problem into two subproblems by setting 
(x + 0.085) equal to 0.215 and -0.215.


Subproblem 1
x + 0.085 = 0.215

Simplifying
x + 0.085 = 0.215

Reorder the terms:
0.085 + x = 0.215

Solving
0.085 + x = 0.215

Solving for variable 'x'.

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

Add '-0.085' to each side of the equation.
0.085 + -0.085 + x = 0.215 + -0.085

Combine like terms: 0.085 + -0.085 = 0.000
0.000 + x = 0.215 + -0.085
x = 0.215 + -0.085

Combine like terms: 0.215 + -0.085 = 0.13
x = 0.13

Simplifying
x = 0.13


Subproblem 2
x + 0.085 = -0.215

Simplifying
x + 0.085 = -0.215

Reorder the terms:
0.085 + x = -0.215

Solving
0.085 + x = -0.215

Solving for variable 'x'.

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

Add '-0.085' to each side of the equation.
0.085 + -0.085 + x = -0.215 + -0.085

Combine like terms: 0.085 + -0.085 = 0.000
0.000 + x = -0.215 + -0.085
x = -0.215 + -0.085

Combine like terms: -0.215 + -0.085 = -0.3
x = -0.3

Simplifying
x = -0.3


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.13, -0.3}

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