0.8X^2+0.2X=0.3

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Solution for 0.8X^2+0.2X=0.3 equation: 


Simplifying
0.8X2 + 0.2X = 0.3

Reorder the terms:
0.2X + 0.8X2 = 0.3

Solving
0.2X + 0.8X2 = 0.3

Solving for variable 'X'.

Reorder the terms:
-0.3 + 0.2X + 0.8X2 = 0.3 + -0.3

Combine like terms: 0.3 + -0.3 = 0.0
-0.3 + 0.2X + 0.8X2 = 0.0

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

Divide each side by '0.8'.
-0.375 + 0.25X + X2 = 0

Move the constant term to the right:

Add '0.375' to each side of the equation.
-0.375 + 0.25X + 0.375 + X2 = 0 + 0.375

Reorder the terms:
-0.375 + 0.375 + 0.25X + X2 = 0 + 0.375

Combine like terms: -0.375 + 0.375 = 0.000
0.000 + 0.25X + X2 = 0 + 0.375
0.25X + X2 = 0 + 0.375

Combine like terms: 0 + 0.375 = 0.375
0.25X + X2 = 0.375

The X term is 0.25X.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25X + 0.015625 + X2 = 0.375 + 0.015625

Reorder the terms:
0.015625 + 0.25X + X2 = 0.375 + 0.015625

Combine like terms: 0.375 + 0.015625 = 0.390625
0.015625 + 0.25X + X2 = 0.390625

Factor a perfect square on the left side:
(X + 0.125)(X + 0.125) = 0.390625

Calculate the square root of the right side: 0.625

Break this problem into two subproblems by setting 
(X + 0.125) equal to 0.625 and -0.625.


Subproblem 1
X + 0.125 = 0.625

Simplifying
X + 0.125 = 0.625

Reorder the terms:
0.125 + X = 0.625

Solving
0.125 + X = 0.625

Solving for variable 'X'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + X = 0.625 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + X = 0.625 + -0.125
X = 0.625 + -0.125

Combine like terms: 0.625 + -0.125 = 0.5
X = 0.5

Simplifying
X = 0.5


Subproblem 2
X + 0.125 = -0.625

Simplifying
X + 0.125 = -0.625

Reorder the terms:
0.125 + X = -0.625

Solving
0.125 + X = -0.625

Solving for variable 'X'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + X = -0.625 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + X = -0.625 + -0.125
X = -0.625 + -0.125

Combine like terms: -0.625 + -0.125 = -0.75
X = -0.75

Simplifying
X = -0.75


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {0.5, -0.75}

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