x^2+0.17x-0.034=0

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Solution for x^2+0.17x-0.034=0 equation:


Simplifying
x2 + 0.17x + -0.034 = 0

Reorder the terms:
-0.034 + 0.17x + x2 = 0

Solving
-0.034 + 0.17x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.034' to each side of the equation.
-0.034 + 0.17x + 0.034 + x2 = 0 + 0.034

Reorder the terms:
-0.034 + 0.034 + 0.17x + x2 = 0 + 0.034

Combine like terms: -0.034 + 0.034 = 0.000
0.000 + 0.17x + x2 = 0 + 0.034
0.17x + x2 = 0 + 0.034

Combine like terms: 0 + 0.034 = 0.034
0.17x + x2 = 0.034

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 = 0.034 + 0.007225

Reorder the terms:
0.007225 + 0.17x + x2 = 0.034 + 0.007225

Combine like terms: 0.034 + 0.007225 = 0.041225
0.007225 + 0.17x + x2 = 0.041225

Factor a perfect square on the left side:
(x + 0.085)(x + 0.085) = 0.041225

Calculate the square root of the right side: 0.203039405

Break this problem into two subproblems by setting 
(x + 0.085) equal to 0.203039405 and -0.203039405.


Subproblem 1
x + 0.085 = 0.203039405

Simplifying
x + 0.085 = 0.203039405

Reorder the terms:
0.085 + x = 0.203039405

Solving
0.085 + x = 0.203039405

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 = 0.203039405 + -0.085

Combine like terms: 0.085 + -0.085 = 0.000
0.000 + x = 0.203039405 + -0.085
x = 0.203039405 + -0.085

Combine like terms: 0.203039405 + -0.085 = 0.118039405
x = 0.118039405

Simplifying
x = 0.118039405


Subproblem 2
x + 0.085 = -0.203039405

Simplifying
x + 0.085 = -0.203039405

Reorder the terms:
0.085 + x = -0.203039405

Solving
0.085 + x = -0.203039405

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 = -0.203039405 + -0.085

Combine like terms: 0.085 + -0.085 = 0.000
0.000 + x = -0.203039405 + -0.085
x = -0.203039405 + -0.085

Combine like terms: -0.203039405 + -0.085 = -0.288039405
x = -0.288039405

Simplifying
x = -0.288039405


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.118039405, -0.288039405}

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