5.833333333x+x^2=0.25

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Solution for 5.833333333x+x^2=0.25 equation: 


Simplifying
5.833333333x + x2 = 0.25

Solving
5.833333333x + x2 = 0.25

Solving for variable 'x'.

Reorder the terms:
-0.25 + 5.833333333x + x2 = 0.25 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
-0.25 + 5.833333333x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + 5.833333333x + 0.25 + x2 = 0.00 + 0.25

Reorder the terms:
-0.25 + 0.25 + 5.833333333x + x2 = 0.00 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + 5.833333333x + x2 = 0.00 + 0.25
5.833333333x + x2 = 0.00 + 0.25

Combine like terms: 0.00 + 0.25 = 0.25
5.833333333x + x2 = 0.25

The x term is 5.833333333x.  Take half its coefficient (2.916666667).
Square it (8.506944446) and add it to both sides.

Add '8.506944446' to each side of the equation.
5.833333333x + 8.506944446 + x2 = 0.25 + 8.506944446

Reorder the terms:
8.506944446 + 5.833333333x + x2 = 0.25 + 8.506944446

Combine like terms: 0.25 + 8.506944446 = 8.756944446
8.506944446 + 5.833333333x + x2 = 8.756944446

Factor a perfect square on the left side:
(x + 2.916666667)(x + 2.916666667) = 8.756944446

Calculate the square root of the right side: 2.959213484

Break this problem into two subproblems by setting 
(x + 2.916666667) equal to 2.959213484 and -2.959213484.


Subproblem 1
x + 2.916666667 = 2.959213484

Simplifying
x + 2.916666667 = 2.959213484

Reorder the terms:
2.916666667 + x = 2.959213484

Solving
2.916666667 + x = 2.959213484

Solving for variable 'x'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + x = 2.959213484 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = 2.959213484 + -2.916666667
x = 2.959213484 + -2.916666667

Combine like terms: 2.959213484 + -2.916666667 = 0.042546817
x = 0.042546817

Simplifying
x = 0.042546817


Subproblem 2
x + 2.916666667 = -2.959213484

Simplifying
x + 2.916666667 = -2.959213484

Reorder the terms:
2.916666667 + x = -2.959213484

Solving
2.916666667 + x = -2.959213484

Solving for variable 'x'.

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

Add '-2.916666667' to each side of the equation.
2.916666667 + -2.916666667 + x = -2.959213484 + -2.916666667

Combine like terms: 2.916666667 + -2.916666667 = 0.000000000
0.000000000 + x = -2.959213484 + -2.916666667
x = -2.959213484 + -2.916666667

Combine like terms: -2.959213484 + -2.916666667 = -5.875880151
x = -5.875880151

Simplifying
x = -5.875880151


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.042546817, -5.875880151}

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