(x^2)+0.08x=0.024

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Solution for (x^2)+0.08x=0.024 equation: 


Simplifying
(x2) + 0.08x = 0.024
x2 + 0.08x = 0.024

Reorder the terms:
0.08x + x2 = 0.024

Solving
0.08x + x2 = 0.024

Solving for variable 'x'.

Reorder the terms:
-0.024 + 0.08x + x2 = 0.024 + -0.024

Combine like terms: 0.024 + -0.024 = 0.000
-0.024 + 0.08x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.024' to each side of the equation.
-0.024 + 0.08x + 0.024 + x2 = 0.000 + 0.024

Reorder the terms:
-0.024 + 0.024 + 0.08x + x2 = 0.000 + 0.024

Combine like terms: -0.024 + 0.024 = 0.000
0.000 + 0.08x + x2 = 0.000 + 0.024
0.08x + x2 = 0.000 + 0.024

Combine like terms: 0.000 + 0.024 = 0.024
0.08x + x2 = 0.024

The x term is 0.08x.  Take half its coefficient (0.04).
Square it (0.0016) and add it to both sides.

Add '0.0016' to each side of the equation.
0.08x + 0.0016 + x2 = 0.024 + 0.0016

Reorder the terms:
0.0016 + 0.08x + x2 = 0.024 + 0.0016

Combine like terms: 0.024 + 0.0016 = 0.0256
0.0016 + 0.08x + x2 = 0.0256

Factor a perfect square on the left side:
(x + 0.04)(x + 0.04) = 0.0256

Calculate the square root of the right side: 0.16

Break this problem into two subproblems by setting 
(x + 0.04) equal to 0.16 and -0.16.


Subproblem 1
x + 0.04 = 0.16

Simplifying
x + 0.04 = 0.16

Reorder the terms:
0.04 + x = 0.16

Solving
0.04 + x = 0.16

Solving for variable 'x'.

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

Add '-0.04' to each side of the equation.
0.04 + -0.04 + x = 0.16 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
0.00 + x = 0.16 + -0.04
x = 0.16 + -0.04

Combine like terms: 0.16 + -0.04 = 0.12
x = 0.12

Simplifying
x = 0.12


Subproblem 2
x + 0.04 = -0.16

Simplifying
x + 0.04 = -0.16

Reorder the terms:
0.04 + x = -0.16

Solving
0.04 + x = -0.16

Solving for variable 'x'.

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

Add '-0.04' to each side of the equation.
0.04 + -0.04 + x = -0.16 + -0.04

Combine like terms: 0.04 + -0.04 = 0.00
0.00 + x = -0.16 + -0.04
x = -0.16 + -0.04

Combine like terms: -0.16 + -0.04 = -0.2
x = -0.2

Simplifying
x = -0.2


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.12, -0.2}

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