0.1x^2-4x+.5=0

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Solution for 0.1x^2-4x+.5=0 equation:


Simplifying
0.1x2 + -4x + 0.5 = 0

Reorder the terms:
0.5 + -4x + 0.1x2 = 0

Solving
0.5 + -4x + 0.1x2 = 0

Solving for variable 'x'.

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

Divide each side by '0.1'.
5 + -40x + x2 = 0

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + -40x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + -40x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -40x + x2 = 0 + -5
-40x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
-40x + x2 = -5

The x term is -40x.  Take half its coefficient (-20).
Square it (400) and add it to both sides.

Add '400' to each side of the equation.
-40x + 400 + x2 = -5 + 400

Reorder the terms:
400 + -40x + x2 = -5 + 400

Combine like terms: -5 + 400 = 395
400 + -40x + x2 = 395

Factor a perfect square on the left side:
(x + -20)(x + -20) = 395

Calculate the square root of the right side: 19.874606914

Break this problem into two subproblems by setting 
(x + -20) equal to 19.874606914 and -19.874606914.

Subproblem 1

x + -20 = 19.874606914 Simplifying x + -20 = 19.874606914 Reorder the terms: -20 + x = 19.874606914 Solving -20 + x = 19.874606914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = 19.874606914 + 20 Combine like terms: -20 + 20 = 0 0 + x = 19.874606914 + 20 x = 19.874606914 + 20 Combine like terms: 19.874606914 + 20 = 39.874606914 x = 39.874606914 Simplifying x = 39.874606914

Subproblem 2

x + -20 = -19.874606914 Simplifying x + -20 = -19.874606914 Reorder the terms: -20 + x = -19.874606914 Solving -20 + x = -19.874606914 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + x = -19.874606914 + 20 Combine like terms: -20 + 20 = 0 0 + x = -19.874606914 + 20 x = -19.874606914 + 20 Combine like terms: -19.874606914 + 20 = 0.125393086 x = 0.125393086 Simplifying x = 0.125393086

Solution

The solution to the problem is based on the solutions from the subproblems. x = {39.874606914, 0.125393086}

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