-0.6x^2+4x+0.5=0

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Solution for -0.6x^2+4x+0.5=0 equation: 


Simplifying
-0.6x2 + 4x + 0.5 = 0

Reorder the terms:
0.5 + 4x + -0.6x2 = 0

Solving
0.5 + 4x + -0.6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.6 the coefficient of the squared term: 

Divide each side by '-0.6'.
-0.8333333333 + -6.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + -6.666666667x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + -6.666666667x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + -6.666666667x + x2 = 0 + 0.8333333333
-6.666666667x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
-6.666666667x + x2 = 0.8333333333

The x term is -6.666666667x.  Take half its coefficient (-3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
-6.666666667x + 11.11111112 + x2 = 0.8333333333 + 11.11111112

Reorder the terms:
11.11111112 + -6.666666667x + x2 = 0.8333333333 + 11.11111112

Combine like terms: 0.8333333333 + 11.11111112 = 11.9444444533
11.11111112 + -6.666666667x + x2 = 11.9444444533

Factor a perfect square on the left side:
(x + -3.333333334)(x + -3.333333334) = 11.9444444533

Calculate the square root of the right side: 3.45607356

Break this problem into two subproblems by setting 
(x + -3.333333334) equal to 3.45607356 and -3.45607356.


Subproblem 1
x + -3.333333334 = 3.45607356

Simplifying
x + -3.333333334 = 3.45607356

Reorder the terms:
-3.333333334 + x = 3.45607356

Solving
-3.333333334 + x = 3.45607356

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = 3.45607356 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = 3.45607356 + 3.333333334
x = 3.45607356 + 3.333333334

Combine like terms: 3.45607356 + 3.333333334 = 6.789406894
x = 6.789406894

Simplifying
x = 6.789406894


Subproblem 2
x + -3.333333334 = -3.45607356

Simplifying
x + -3.333333334 = -3.45607356

Reorder the terms:
-3.333333334 + x = -3.45607356

Solving
-3.333333334 + x = -3.45607356

Solving for variable 'x'.

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

Add '3.333333334' to each side of the equation.
-3.333333334 + 3.333333334 + x = -3.45607356 + 3.333333334

Combine like terms: -3.333333334 + 3.333333334 = 0.000000000
0.000000000 + x = -3.45607356 + 3.333333334
x = -3.45607356 + 3.333333334

Combine like terms: -3.45607356 + 3.333333334 = -0.122740226
x = -0.122740226

Simplifying
x = -0.122740226


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.789406894, -0.122740226}

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