50-.25x=3x^2

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Solution for 50-.25x=3x^2 equation: 


Simplifying
50 + -0.25x = 3x2

Solving
50 + -0.25x = 3x2

Solving for variable 'x'.

Combine like terms: 3x2 + -3x2 = 0
50 + -0.25x + -3x2 = 0

Begin completing the square.  Divide all terms by
-3 the coefficient of the squared term: 

Divide each side by '-3'.
-16.66666667 + 0.08333333333x + x2 = 0

Move the constant term to the right:

Add '16.66666667' to each side of the equation.
-16.66666667 + 0.08333333333x + 16.66666667 + x2 = 0 + 16.66666667

Reorder the terms:
-16.66666667 + 16.66666667 + 0.08333333333x + x2 = 0 + 16.66666667

Combine like terms: -16.66666667 + 16.66666667 = 0.00000000
0.00000000 + 0.08333333333x + x2 = 0 + 16.66666667
0.08333333333x + x2 = 0 + 16.66666667

Combine like terms: 0 + 16.66666667 = 16.66666667
0.08333333333x + x2 = 16.66666667

The x term is 0.08333333333x.  Take half its coefficient (0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
0.08333333333x + 0.001736111111 + x2 = 16.66666667 + 0.001736111111

Reorder the terms:
0.001736111111 + 0.08333333333x + x2 = 16.66666667 + 0.001736111111

Combine like terms: 16.66666667 + 0.001736111111 = 16.668402781111
0.001736111111 + 0.08333333333x + x2 = 16.668402781111

Factor a perfect square on the left side:
(x + 0.04166666667)(x + 0.04166666667) = 16.668402781111

Calculate the square root of the right side: 4.082695529

Break this problem into two subproblems by setting 
(x + 0.04166666667) equal to 4.082695529 and -4.082695529.


Subproblem 1
x + 0.04166666667 = 4.082695529

Simplifying
x + 0.04166666667 = 4.082695529

Reorder the terms:
0.04166666667 + x = 4.082695529

Solving
0.04166666667 + x = 4.082695529

Solving for variable 'x'.

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

Add '-0.04166666667' to each side of the equation.
0.04166666667 + -0.04166666667 + x = 4.082695529 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + x = 4.082695529 + -0.04166666667
x = 4.082695529 + -0.04166666667

Combine like terms: 4.082695529 + -0.04166666667 = 4.04102886233
x = 4.04102886233

Simplifying
x = 4.04102886233


Subproblem 2
x + 0.04166666667 = -4.082695529

Simplifying
x + 0.04166666667 = -4.082695529

Reorder the terms:
0.04166666667 + x = -4.082695529

Solving
0.04166666667 + x = -4.082695529

Solving for variable 'x'.

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

Add '-0.04166666667' to each side of the equation.
0.04166666667 + -0.04166666667 + x = -4.082695529 + -0.04166666667

Combine like terms: 0.04166666667 + -0.04166666667 = 0.00000000000
0.00000000000 + x = -4.082695529 + -0.04166666667
x = -4.082695529 + -0.04166666667

Combine like terms: -4.082695529 + -0.04166666667 = -4.12436219567
x = -4.12436219567

Simplifying
x = -4.12436219567


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.04102886233, -4.12436219567}

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