0.01x^2+0.006x-0.08=0

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Solution for 0.01x^2+0.006x-0.08=0 equation: 


Simplifying
0.01x2 + 0.006x + -0.08 = 0

Reorder the terms:
-0.08 + 0.006x + 0.01x2 = 0

Solving
-0.08 + 0.006x + 0.01x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
0.01 the coefficient of the squared term: 

Divide each side by '0.01'.
-8 + 0.6x + x2 = 0

Move the constant term to the right:

Add '8' to each side of the equation.
-8 + 0.6x + 8 + x2 = 0 + 8

Reorder the terms:
-8 + 8 + 0.6x + x2 = 0 + 8

Combine like terms: -8 + 8 = 0
0 + 0.6x + x2 = 0 + 8
0.6x + x2 = 0 + 8

Combine like terms: 0 + 8 = 8
0.6x + x2 = 8

The x term is 0.6x.  Take half its coefficient (0.3).
Square it (0.09) and add it to both sides.

Add '0.09' to each side of the equation.
0.6x + 0.09 + x2 = 8 + 0.09

Reorder the terms:
0.09 + 0.6x + x2 = 8 + 0.09

Combine like terms: 8 + 0.09 = 8.09
0.09 + 0.6x + x2 = 8.09

Factor a perfect square on the left side:
(x + 0.3)(x + 0.3) = 8.09

Calculate the square root of the right side: 2.844292531

Break this problem into two subproblems by setting 
(x + 0.3) equal to 2.844292531 and -2.844292531.


Subproblem 1
x + 0.3 = 2.844292531

Simplifying
x + 0.3 = 2.844292531

Reorder the terms:
0.3 + x = 2.844292531

Solving
0.3 + x = 2.844292531

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = 2.844292531 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = 2.844292531 + -0.3
x = 2.844292531 + -0.3

Combine like terms: 2.844292531 + -0.3 = 2.544292531
x = 2.544292531

Simplifying
x = 2.544292531


Subproblem 2
x + 0.3 = -2.844292531

Simplifying
x + 0.3 = -2.844292531

Reorder the terms:
0.3 + x = -2.844292531

Solving
0.3 + x = -2.844292531

Solving for variable 'x'.

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

Add '-0.3' to each side of the equation.
0.3 + -0.3 + x = -2.844292531 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
0.0 + x = -2.844292531 + -0.3
x = -2.844292531 + -0.3

Combine like terms: -2.844292531 + -0.3 = -3.144292531
x = -3.144292531

Simplifying
x = -3.144292531


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.544292531, -3.144292531}

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