3x^2+x-98=0

Solution for 3x^2+x-98=0 equation:

Simplifying
3x2 + x + -98 = 0

Reorder the terms:
-98 + x + 3x2 = 0

Solving
-98 + x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-32.66666667 + 0.3333333333x + x2 = 0

Move the constant term to the right:

Add '32.66666667' to each side of the equation.
-32.66666667 + 0.3333333333x + 32.66666667 + x2 = 0 + 32.66666667

Reorder the terms:
-32.66666667 + 32.66666667 + 0.3333333333x + x2 = 0 + 32.66666667

Combine like terms: -32.66666667 + 32.66666667 = 0.00000000
0.00000000 + 0.3333333333x + x2 = 0 + 32.66666667
0.3333333333x + x2 = 0 + 32.66666667

Combine like terms: 0 + 32.66666667 = 32.66666667
0.3333333333x + x2 = 32.66666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333x + 0.25 + x2 = 32.66666667 + 0.25

Reorder the terms:
0.25 + 0.3333333333x + x2 = 32.66666667 + 0.25

Combine like terms: 32.66666667 + 0.25 = 32.91666667
0.25 + 0.3333333333x + x2 = 32.91666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 32.91666667

Calculate the square root of the right side: 5.737304826

Break this problem into two subproblems by setting 
(x + 0.5) equal to 5.737304826 and -5.737304826.

Subproblem 1
x + 0.5 = 5.737304826

Simplifying
x + 0.5 = 5.737304826

Reorder the terms:
0.5 + x = 5.737304826

Solving
0.5 + x = 5.737304826

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 5.737304826 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 5.737304826 + -0.5
x = 5.737304826 + -0.5

Combine like terms: 5.737304826 + -0.5 = 5.237304826
x = 5.237304826

Simplifying
x = 5.237304826

Subproblem 2
x + 0.5 = -5.737304826

Simplifying
x + 0.5 = -5.737304826

Reorder the terms:
0.5 + x = -5.737304826

Solving
0.5 + x = -5.737304826

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -5.737304826 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -5.737304826 + -0.5
x = -5.737304826 + -0.5

Combine like terms: -5.737304826 + -0.5 = -6.237304826
x = -6.237304826

Simplifying
x = -6.237304826

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.237304826, -6.237304826}