12x^2+7x-4=0

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Solution for 12x^2+7x-4=0 equation: 


Simplifying
12x2 + 7x + -4 = 0

Reorder the terms:
-4 + 7x + 12x2 = 0

Solving
-4 + 7x + 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'.
-0.3333333333 + 0.5833333333x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + 0.5833333333x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + 0.5833333333x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + 0.5833333333x + x2 = 0 + 0.3333333333
0.5833333333x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
0.5833333333x + x2 = 0.3333333333

The x term is 0.5833333333x.  Take half its coefficient (0.2916666667).
Square it (0.08506944446) and add it to both sides.

Add '0.08506944446' to each side of the equation.
0.5833333333x + 0.08506944446 + x2 = 0.3333333333 + 0.08506944446

Reorder the terms:
0.08506944446 + 0.5833333333x + x2 = 0.3333333333 + 0.08506944446

Combine like terms: 0.3333333333 + 0.08506944446 = 0.41840277776
0.08506944446 + 0.5833333333x + x2 = 0.41840277776

Factor a perfect square on the left side:
(x + 0.2916666667)(x + 0.2916666667) = 0.41840277776

Calculate the square root of the right side: 0.646840612

Break this problem into two subproblems by setting 
(x + 0.2916666667) equal to 0.646840612 and -0.646840612.


Subproblem 1
x + 0.2916666667 = 0.646840612

Simplifying
x + 0.2916666667 = 0.646840612

Reorder the terms:
0.2916666667 + x = 0.646840612

Solving
0.2916666667 + x = 0.646840612

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = 0.646840612 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = 0.646840612 + -0.2916666667
x = 0.646840612 + -0.2916666667

Combine like terms: 0.646840612 + -0.2916666667 = 0.3551739453
x = 0.3551739453

Simplifying
x = 0.3551739453


Subproblem 2
x + 0.2916666667 = -0.646840612

Simplifying
x + 0.2916666667 = -0.646840612

Reorder the terms:
0.2916666667 + x = -0.646840612

Solving
0.2916666667 + x = -0.646840612

Solving for variable 'x'.

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

Add '-0.2916666667' to each side of the equation.
0.2916666667 + -0.2916666667 + x = -0.646840612 + -0.2916666667

Combine like terms: 0.2916666667 + -0.2916666667 = 0.0000000000
0.0000000000 + x = -0.646840612 + -0.2916666667
x = -0.646840612 + -0.2916666667

Combine like terms: -0.646840612 + -0.2916666667 = -0.9385072787
x = -0.9385072787

Simplifying
x = -0.9385072787


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.3551739453, -0.9385072787}

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