12x^2+5x-98=0

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Solution for 12x^2+5x-98=0 equation: 


Simplifying
12x2 + 5x + -98 = 0

Reorder the terms:
-98 + 5x + 12x2 = 0

Solving
-98 + 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'.
-8.166666667 + 0.4166666667x + x2 = 0

Move the constant term to the right:

Add '8.166666667' to each side of the equation.
-8.166666667 + 0.4166666667x + 8.166666667 + x2 = 0 + 8.166666667

Reorder the terms:
-8.166666667 + 8.166666667 + 0.4166666667x + x2 = 0 + 8.166666667

Combine like terms: -8.166666667 + 8.166666667 = 0.000000000
0.000000000 + 0.4166666667x + x2 = 0 + 8.166666667
0.4166666667x + x2 = 0 + 8.166666667

Combine like terms: 0 + 8.166666667 = 8.166666667
0.4166666667x + x2 = 8.166666667

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 = 8.166666667 + 0.04340277781

Reorder the terms:
0.04340277781 + 0.4166666667x + x2 = 8.166666667 + 0.04340277781

Combine like terms: 8.166666667 + 0.04340277781 = 8.21006944481
0.04340277781 + 0.4166666667x + x2 = 8.21006944481

Factor a perfect square on the left side:
(x + 0.2083333334)(x + 0.2083333334) = 8.21006944481

Calculate the square root of the right side: 2.865321875

Break this problem into two subproblems by setting 
(x + 0.2083333334) equal to 2.865321875 and -2.865321875.


Subproblem 1
x + 0.2083333334 = 2.865321875

Simplifying
x + 0.2083333334 = 2.865321875

Reorder the terms:
0.2083333334 + x = 2.865321875

Solving
0.2083333334 + x = 2.865321875

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 = 2.865321875 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = 2.865321875 + -0.2083333334
x = 2.865321875 + -0.2083333334

Combine like terms: 2.865321875 + -0.2083333334 = 2.6569885416
x = 2.6569885416

Simplifying
x = 2.6569885416


Subproblem 2
x + 0.2083333334 = -2.865321875

Simplifying
x + 0.2083333334 = -2.865321875

Reorder the terms:
0.2083333334 + x = -2.865321875

Solving
0.2083333334 + x = -2.865321875

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 = -2.865321875 + -0.2083333334

Combine like terms: 0.2083333334 + -0.2083333334 = 0.0000000000
0.0000000000 + x = -2.865321875 + -0.2083333334
x = -2.865321875 + -0.2083333334

Combine like terms: -2.865321875 + -0.2083333334 = -3.0736552084
x = -3.0736552084

Simplifying
x = -3.0736552084


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.6569885416, -3.0736552084}

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