(5x^2)-4x=0.1

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Solution for (5x^2)-4x=0.1 equation:


Simplifying
(5x2) + -4x = 0.1

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

Solving
-4x + (5x2) = 0.1

Solving for variable 'x'.

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

Combine like terms: 0.1 + -0.1 = 0.0
-0.1 + -4x + (5x2) = 0.0

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 = 0.0

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 + 0.02

Reorder the terms:
-0.02 + 0.02 + -0.8x + x2 = 0.0 + 0.02

Combine like terms: -0.02 + 0.02 = 0.00
0.00 + -0.8x + x2 = 0.0 + 0.02
-0.8x + x2 = 0.0 + 0.02

Combine like terms: 0.0 + 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 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 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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