12x^2+5x-94=0

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Solution for 12x^2+5x-94=0 equation: 


Simplifying
12x2 + 5x + -94 = 0

Reorder the terms:
-94 + 5x + 12x2 = 0

Solving
-94 + 5x + 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'.
-7.833333333 + 0.4166666667x + x2 = 0

Move the constant term to the right:

Add '7.833333333' to each side of the equation.
-7.833333333 + 0.4166666667x + 7.833333333 + x2 = 0 + 7.833333333

Reorder the terms:
-7.833333333 + 7.833333333 + 0.4166666667x + x2 = 0 + 7.833333333

Combine like terms: -7.833333333 + 7.833333333 = 0.000000000
0.000000000 + 0.4166666667x + x2 = 0 + 7.833333333
0.4166666667x + x2 = 0 + 7.833333333

Combine like terms: 0 + 7.833333333 = 7.833333333
0.4166666667x + x2 = 7.833333333

The x term is 0.4166666667x.  Take half its coefficient (0.2083333334).
Square it (0.04340277781) and add it to both sides.

Add '0.04340277781' to each side of the equation.
0.4166666667x + 0.04340277781 + x2 = 7.833333333 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667x + x2 = 7.833333333 + 0.04340277781

Combine like terms: 7.833333333 + 0.04340277781 = 7.87673611081
0.04340277781 + 0.4166666667x + x2 = 7.87673611081

Factor a perfect square on the left side:
(x + 0.2083333334)(x + 0.2083333334) = 7.87673611081

Calculate the square root of the right side: 2.806552353

Break this problem into two subproblems by setting 
(x + 0.2083333334) equal to 2.806552353 and -2.806552353.


Subproblem 1
x + 0.2083333334 = 2.806552353

Simplifying
x + 0.2083333334 = 2.806552353

Reorder the terms:
0.2083333334 + x = 2.806552353

Solving
0.2083333334 + x = 2.806552353

Solving for variable 'x'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + x = 2.806552353 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = 2.806552353 + -0.2083333334
x = 2.806552353 + -0.2083333334

Combine like terms: 2.806552353 + -0.2083333334 = 2.5982190196
x = 2.5982190196

Simplifying
x = 2.5982190196


Subproblem 2
x + 0.2083333334 = -2.806552353

Simplifying
x + 0.2083333334 = -2.806552353

Reorder the terms:
0.2083333334 + x = -2.806552353

Solving
0.2083333334 + x = -2.806552353

Solving for variable 'x'.

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

Add '-0.2083333334' to each side of the equation.
0.2083333334 + -0.2083333334 + x = -2.806552353 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = -2.806552353 + -0.2083333334
x = -2.806552353 + -0.2083333334

Combine like terms: -2.806552353 + -0.2083333334 = -3.0148856864
x = -3.0148856864

Simplifying
x = -3.0148856864


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.5982190196, -3.0148856864}

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