12x^2-34x+5=0

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Solution for 12x^2-34x+5=0 equation:


Simplifying
12x2 + -34x + 5 = 0

Reorder the terms:
5 + -34x + 12x2 = 0

Solving
5 + -34x + 12x2 = 0

Solving for variable 'x'.

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

Divide each side by '12'.
0.4166666667 + -2.833333333x + x2 = 0

Move the constant term to the right:

Add '-0.4166666667' to each side of the equation.
0.4166666667 + -2.833333333x + -0.4166666667 + x2 = 0 + -0.4166666667

Reorder the terms:
0.4166666667 + -0.4166666667 + -2.833333333x + x2 = 0 + -0.4166666667

Combine like terms: 0.4166666667 + -0.4166666667 = 0.0000000000
0.0000000000 + -2.833333333x + x2 = 0 + -0.4166666667
-2.833333333x + x2 = 0 + -0.4166666667

Combine like terms: 0 + -0.4166666667 = -0.4166666667
-2.833333333x + x2 = -0.4166666667

The x term is -2.833333333x.  Take half its coefficient (-1.416666667).
Square it (2.006944445) and add it to both sides.

Add '2.006944445' to each side of the equation.
-2.833333333x + 2.006944445 + x2 = -0.4166666667 + 2.006944445

Reorder the terms:
2.006944445 + -2.833333333x + x2 = -0.4166666667 + 2.006944445

Combine like terms: -0.4166666667 + 2.006944445 = 1.5902777783
2.006944445 + -2.833333333x + x2 = 1.5902777783

Factor a perfect square on the left side:
(x + -1.416666667)(x + -1.416666667) = 1.5902777783

Calculate the square root of the right side: 1.261062163

Break this problem into two subproblems by setting 
(x + -1.416666667) equal to 1.261062163 and -1.261062163.


Subproblem 1
x + -1.416666667 = 1.261062163

Simplifying
x + -1.416666667 = 1.261062163

Reorder the terms:
-1.416666667 + x = 1.261062163

Solving
-1.416666667 + x = 1.261062163

Solving for variable 'x'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + x = 1.261062163 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + x = 1.261062163 + 1.416666667
x = 1.261062163 + 1.416666667

Combine like terms: 1.261062163 + 1.416666667 = 2.67772883
x = 2.67772883

Simplifying
x = 2.67772883


Subproblem 2
x + -1.416666667 = -1.261062163

Simplifying
x + -1.416666667 = -1.261062163

Reorder the terms:
-1.416666667 + x = -1.261062163

Solving
-1.416666667 + x = -1.261062163

Solving for variable 'x'.

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

Add '1.416666667' to each side of the equation.
-1.416666667 + 1.416666667 + x = -1.261062163 + 1.416666667

Combine like terms: -1.416666667 + 1.416666667 = 0.000000000
0.000000000 + x = -1.261062163 + 1.416666667
x = -1.261062163 + 1.416666667

Combine like terms: -1.261062163 + 1.416666667 = 0.155604504
x = 0.155604504

Simplifying
x = 0.155604504


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.67772883, 0.155604504}

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