x^2+0.03x-0.0006=0

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Solution for x^2+0.03x-0.0006=0 equation:


Simplifying
x2 + 0.03x + -0.0006 = 0

Reorder the terms:
-0.0006 + 0.03x + x2 = 0

Solving
-0.0006 + 0.03x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '0.0006' to each side of the equation.
-0.0006 + 0.03x + 0.0006 + x2 = 0 + 0.0006

Reorder the terms:
-0.0006 + 0.0006 + 0.03x + x2 = 0 + 0.0006

Combine like terms: -0.0006 + 0.0006 = 0.0000
0.0000 + 0.03x + x2 = 0 + 0.0006
0.03x + x2 = 0 + 0.0006

Combine like terms: 0 + 0.0006 = 0.0006
0.03x + x2 = 0.0006

The x term is 0.03x.  Take half its coefficient (0.015).
Square it (0.000225) and add it to both sides.

Add '0.000225' to each side of the equation.
0.03x + 0.000225 + x2 = 0.0006 + 0.000225

Reorder the terms:
0.000225 + 0.03x + x2 = 0.0006 + 0.000225

Combine like terms: 0.0006 + 0.000225 = 0.000825
0.000225 + 0.03x + x2 = 0.000825

Factor a perfect square on the left side:
(x + 0.015)(x + 0.015) = 0.000825

Calculate the square root of the right side: 0.028722813

Break this problem into two subproblems by setting 
(x + 0.015) equal to 0.028722813 and -0.028722813.


Subproblem 1
x + 0.015 = 0.028722813

Simplifying
x + 0.015 = 0.028722813

Reorder the terms:
0.015 + x = 0.028722813

Solving
0.015 + x = 0.028722813

Solving for variable 'x'.

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

Add '-0.015' to each side of the equation.
0.015 + -0.015 + x = 0.028722813 + -0.015

Combine like terms: 0.015 + -0.015 = 0.000
0.000 + x = 0.028722813 + -0.015
x = 0.028722813 + -0.015

Combine like terms: 0.028722813 + -0.015 = 0.013722813
x = 0.013722813

Simplifying
x = 0.013722813


Subproblem 2
x + 0.015 = -0.028722813

Simplifying
x + 0.015 = -0.028722813

Reorder the terms:
0.015 + x = -0.028722813

Solving
0.015 + x = -0.028722813

Solving for variable 'x'.

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

Add '-0.015' to each side of the equation.
0.015 + -0.015 + x = -0.028722813 + -0.015

Combine like terms: 0.015 + -0.015 = 0.000
0.000 + x = -0.028722813 + -0.015
x = -0.028722813 + -0.015

Combine like terms: -0.028722813 + -0.015 = -0.043722813
x = -0.043722813

Simplifying
x = -0.043722813


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.013722813, -0.043722813}

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