-x^2+5.667x+3.334=0

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Solution for -x^2+5.667x+3.334=0 equation: 


Simplifying
-1x2 + 5.667x + 3.334 = 0

Reorder the terms:
3.334 + 5.667x + -1x2 = 0

Solving
3.334 + 5.667x + -1x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3.334 + -5.667x + x2 = 0

Move the constant term to the right:

Add '3.334' to each side of the equation.
-3.334 + -5.667x + 3.334 + x2 = 0 + 3.334

Reorder the terms:
-3.334 + 3.334 + -5.667x + x2 = 0 + 3.334

Combine like terms: -3.334 + 3.334 = 0.000
0.000 + -5.667x + x2 = 0 + 3.334
-5.667x + x2 = 0 + 3.334

Combine like terms: 0 + 3.334 = 3.334
-5.667x + x2 = 3.334

The x term is -5.667x.  Take half its coefficient (-2.8335).
Square it (8.02872225) and add it to both sides.

Add '8.02872225' to each side of the equation.
-5.667x + 8.02872225 + x2 = 3.334 + 8.02872225

Reorder the terms:
8.02872225 + -5.667x + x2 = 3.334 + 8.02872225

Combine like terms: 3.334 + 8.02872225 = 11.36272225
8.02872225 + -5.667x + x2 = 11.36272225

Factor a perfect square on the left side:
(x + -2.8335)(x + -2.8335) = 11.36272225

Calculate the square root of the right side: 3.370863725

Break this problem into two subproblems by setting 
(x + -2.8335) equal to 3.370863725 and -3.370863725.


Subproblem 1
x + -2.8335 = 3.370863725

Simplifying
x + -2.8335 = 3.370863725

Reorder the terms:
-2.8335 + x = 3.370863725

Solving
-2.8335 + x = 3.370863725

Solving for variable 'x'.

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

Add '2.8335' to each side of the equation.
-2.8335 + 2.8335 + x = 3.370863725 + 2.8335

Combine like terms: -2.8335 + 2.8335 = 0.0000
0.0000 + x = 3.370863725 + 2.8335
x = 3.370863725 + 2.8335

Combine like terms: 3.370863725 + 2.8335 = 6.204363725
x = 6.204363725

Simplifying
x = 6.204363725


Subproblem 2
x + -2.8335 = -3.370863725

Simplifying
x + -2.8335 = -3.370863725

Reorder the terms:
-2.8335 + x = -3.370863725

Solving
-2.8335 + x = -3.370863725

Solving for variable 'x'.

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

Add '2.8335' to each side of the equation.
-2.8335 + 2.8335 + x = -3.370863725 + 2.8335

Combine like terms: -2.8335 + 2.8335 = 0.0000
0.0000 + x = -3.370863725 + 2.8335
x = -3.370863725 + 2.8335

Combine like terms: -3.370863725 + 2.8335 = -0.537363725
x = -0.537363725

Simplifying
x = -0.537363725


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.204363725, -0.537363725}

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