x^2=0.04731+0.083x

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Solution for x^2=0.04731+0.083x equation: 


Simplifying
x2 = 0.04731 + 0.083x

Solving
x2 = 0.04731 + 0.083x

Solving for variable 'x'.

Reorder the terms:
-0.04731 + -0.083x + x2 = 0.04731 + 0.083x + -0.04731 + -0.083x

Reorder the terms:
-0.04731 + -0.083x + x2 = 0.04731 + -0.04731 + 0.083x + -0.083x

Combine like terms: 0.04731 + -0.04731 = 0.00000
-0.04731 + -0.083x + x2 = 0.00000 + 0.083x + -0.083x
-0.04731 + -0.083x + x2 = 0.083x + -0.083x

Combine like terms: 0.083x + -0.083x = 0.000
-0.04731 + -0.083x + x2 = 0.000

Begin completing the square.

Move the constant term to the right:

Add '0.04731' to each side of the equation.
-0.04731 + -0.083x + 0.04731 + x2 = 0.000 + 0.04731

Reorder the terms:
-0.04731 + 0.04731 + -0.083x + x2 = 0.000 + 0.04731

Combine like terms: -0.04731 + 0.04731 = 0.00000
0.00000 + -0.083x + x2 = 0.000 + 0.04731
-0.083x + x2 = 0.000 + 0.04731

Combine like terms: 0.000 + 0.04731 = 0.04731
-0.083x + x2 = 0.04731

The x term is -0.083x.  Take half its coefficient (-0.0415).
Square it (0.00172225) and add it to both sides.

Add '0.00172225' to each side of the equation.
-0.083x + 0.00172225 + x2 = 0.04731 + 0.00172225

Reorder the terms:
0.00172225 + -0.083x + x2 = 0.04731 + 0.00172225

Combine like terms: 0.04731 + 0.00172225 = 0.04903225
0.00172225 + -0.083x + x2 = 0.04903225

Factor a perfect square on the left side:
(x + -0.0415)(x + -0.0415) = 0.04903225

Calculate the square root of the right side: 0.22143227

Break this problem into two subproblems by setting 
(x + -0.0415) equal to 0.22143227 and -0.22143227.


Subproblem 1
x + -0.0415 = 0.22143227

Simplifying
x + -0.0415 = 0.22143227

Reorder the terms:
-0.0415 + x = 0.22143227

Solving
-0.0415 + x = 0.22143227

Solving for variable 'x'.

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

Add '0.0415' to each side of the equation.
-0.0415 + 0.0415 + x = 0.22143227 + 0.0415

Combine like terms: -0.0415 + 0.0415 = 0.0000
0.0000 + x = 0.22143227 + 0.0415
x = 0.22143227 + 0.0415

Combine like terms: 0.22143227 + 0.0415 = 0.26293227
x = 0.26293227

Simplifying
x = 0.26293227


Subproblem 2
x + -0.0415 = -0.22143227

Simplifying
x + -0.0415 = -0.22143227

Reorder the terms:
-0.0415 + x = -0.22143227

Solving
-0.0415 + x = -0.22143227

Solving for variable 'x'.

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

Add '0.0415' to each side of the equation.
-0.0415 + 0.0415 + x = -0.22143227 + 0.0415

Combine like terms: -0.0415 + 0.0415 = 0.0000
0.0000 + x = -0.22143227 + 0.0415
x = -0.22143227 + 0.0415

Combine like terms: -0.22143227 + 0.0415 = -0.17993227
x = -0.17993227

Simplifying
x = -0.17993227


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.26293227, -0.17993227}

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