12x^2+13x-30=0

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Solution for 12x^2+13x-30=0 equation: 


Simplifying
12x2 + 13x + -30 = 0

Reorder the terms:
-30 + 13x + 12x2 = 0

Solving
-30 + 13x + 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'.
-2.5 + 1.083333333x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 1.083333333x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 1.083333333x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 1.083333333x + x2 = 0 + 2.5
1.083333333x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
1.083333333x + x2 = 2.5

The x term is 1.083333333x.  Take half its coefficient (0.5416666665).
Square it (0.2934027776) and add it to both sides.

Add '0.2934027776' to each side of the equation.
1.083333333x + 0.2934027776 + x2 = 2.5 + 0.2934027776

Reorder the terms:
0.2934027776 + 1.083333333x + x2 = 2.5 + 0.2934027776

Combine like terms: 2.5 + 0.2934027776 = 2.7934027776
0.2934027776 + 1.083333333x + x2 = 2.7934027776

Factor a perfect square on the left side:
(x + 0.5416666665)(x + 0.5416666665) = 2.7934027776

Calculate the square root of the right side: 1.671347593

Break this problem into two subproblems by setting 
(x + 0.5416666665) equal to 1.671347593 and -1.671347593.


Subproblem 1
x + 0.5416666665 = 1.671347593

Simplifying
x + 0.5416666665 = 1.671347593

Reorder the terms:
0.5416666665 + x = 1.671347593

Solving
0.5416666665 + x = 1.671347593

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = 1.671347593 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = 1.671347593 + -0.5416666665
x = 1.671347593 + -0.5416666665

Combine like terms: 1.671347593 + -0.5416666665 = 1.1296809265
x = 1.1296809265

Simplifying
x = 1.1296809265


Subproblem 2
x + 0.5416666665 = -1.671347593

Simplifying
x + 0.5416666665 = -1.671347593

Reorder the terms:
0.5416666665 + x = -1.671347593

Solving
0.5416666665 + x = -1.671347593

Solving for variable 'x'.

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

Add '-0.5416666665' to each side of the equation.
0.5416666665 + -0.5416666665 + x = -1.671347593 + -0.5416666665

Combine like terms: 0.5416666665 + -0.5416666665 = 0.0000000000
0.0000000000 + x = -1.671347593 + -0.5416666665
x = -1.671347593 + -0.5416666665

Combine like terms: -1.671347593 + -0.5416666665 = -2.2130142595
x = -2.2130142595

Simplifying
x = -2.2130142595


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.1296809265, -2.2130142595}

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