12x^2-60x+58=0

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Solution for 12x^2-60x+58=0 equation: 


Simplifying
12x2 + -60x + 58 = 0

Reorder the terms:
58 + -60x + 12x2 = 0

Solving
58 + -60x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(29 + -30x + 6x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(29 + -30x + 6x2)' equal to zero and attempt to solve:

Simplifying
29 + -30x + 6x2 = 0

Solving
29 + -30x + 6x2 = 0

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

Divide each side by '6'.
4.833333333 + -5x + x2 = 0

Move the constant term to the right:

Add '-4.833333333' to each side of the equation.
4.833333333 + -5x + -4.833333333 + x2 = 0 + -4.833333333

Reorder the terms:
4.833333333 + -4.833333333 + -5x + x2 = 0 + -4.833333333

Combine like terms: 4.833333333 + -4.833333333 = 0.000000000
0.000000000 + -5x + x2 = 0 + -4.833333333
-5x + x2 = 0 + -4.833333333

Combine like terms: 0 + -4.833333333 = -4.833333333
-5x + x2 = -4.833333333

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = -4.833333333 + 6.25

Reorder the terms:
6.25 + -5x + x2 = -4.833333333 + 6.25

Combine like terms: -4.833333333 + 6.25 = 1.416666667
6.25 + -5x + x2 = 1.416666667

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 1.416666667

Calculate the square root of the right side: 1.190238072

Break this problem into two subproblems by setting 
(x + -2.5) equal to 1.190238072 and -1.190238072.


Subproblem 1
x + -2.5 = 1.190238072

Simplifying
x + -2.5 = 1.190238072

Reorder the terms:
-2.5 + x = 1.190238072

Solving
-2.5 + x = 1.190238072

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 1.190238072 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 1.190238072 + 2.5
x = 1.190238072 + 2.5

Combine like terms: 1.190238072 + 2.5 = 3.690238072
x = 3.690238072

Simplifying
x = 3.690238072


Subproblem 2
x + -2.5 = -1.190238072

Simplifying
x + -2.5 = -1.190238072

Reorder the terms:
-2.5 + x = -1.190238072

Solving
-2.5 + x = -1.190238072

Solving for variable 'x'.

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

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -1.190238072 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -1.190238072 + 2.5
x = -1.190238072 + 2.5

Combine like terms: -1.190238072 + 2.5 = 1.309761928
x = 1.309761928

Simplifying
x = 1.309761928


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.690238072, 1.309761928}
Solution
x = {3.690238072, 1.309761928}

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