0.1=x(5x-4)

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Solution for 0.1=x(5x-4) equation: 


Simplifying
0.1 = x(5x + -4)

Reorder the terms:
0.1 = x(-4 + 5x)
0.1 = (-4 * x + 5x * x)
0.1 = (-4x + 5x2)

Solving
0.1 = -4x + 5x2

Solving for variable 'x'.

Reorder the terms:
0.1 + 4x + -5x2 = -4x + 4x + 5x2 + -5x2

Combine like terms: -4x + 4x = 0
0.1 + 4x + -5x2 = 0 + 5x2 + -5x2
0.1 + 4x + -5x2 = 5x2 + -5x2

Combine like terms: 5x2 + -5x2 = 0
0.1 + 4x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-0.02 + -0.8x + x2 = 0

Move the constant term to the right:

Add '0.02' to each side of the equation.
-0.02 + -0.8x + 0.02 + x2 = 0 + 0.02

Reorder the terms:
-0.02 + 0.02 + -0.8x + x2 = 0 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + -0.8x + x2 = 0 + 0.02
-0.8x + x2 = 0 + 0.02

Combine like terms: 0 + 0.02 = 0.02
-0.8x + x2 = 0.02

The x term is -0.8x.  Take half its coefficient (-0.4).
Square it (0.16) and add it to both sides.

Add '0.16' to each side of the equation.
-0.8x + 0.16 + x2 = 0.02 + 0.16

Reorder the terms:
0.16 + -0.8x + x2 = 0.02 + 0.16

Combine like terms: 0.02 + 0.16 = 0.18
0.16 + -0.8x + x2 = 0.18

Factor a perfect square on the left side:
(x + -0.4)(x + -0.4) = 0.18

Calculate the square root of the right side: 0.424264069

Break this problem into two subproblems by setting 
(x + -0.4) equal to 0.424264069 and -0.424264069.


Subproblem 1
x + -0.4 = 0.424264069

Simplifying
x + -0.4 = 0.424264069

Reorder the terms:
-0.4 + x = 0.424264069

Solving
-0.4 + x = 0.424264069

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = 0.424264069 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = 0.424264069 + 0.4
x = 0.424264069 + 0.4

Combine like terms: 0.424264069 + 0.4 = 0.824264069
x = 0.824264069

Simplifying
x = 0.824264069


Subproblem 2
x + -0.4 = -0.424264069

Simplifying
x + -0.4 = -0.424264069

Reorder the terms:
-0.4 + x = -0.424264069

Solving
-0.4 + x = -0.424264069

Solving for variable 'x'.

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

Add '0.4' to each side of the equation.
-0.4 + 0.4 + x = -0.424264069 + 0.4

Combine like terms: -0.4 + 0.4 = 0.0
0.0 + x = -0.424264069 + 0.4
x = -0.424264069 + 0.4

Combine like terms: -0.424264069 + 0.4 = -0.024264069
x = -0.024264069

Simplifying
x = -0.024264069


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.824264069, -0.024264069}

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