3x^2-2x-49=0

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Solution for 3x^2-2x-49=0 equation: 


Simplifying
3x2 + -2x + -49 = 0

Reorder the terms:
-49 + -2x + 3x2 = 0

Solving
-49 + -2x + 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'.
-16.33333333 + -0.6666666667x + x2 = 0

Move the constant term to the right:

Add '16.33333333' to each side of the equation.
-16.33333333 + -0.6666666667x + 16.33333333 + x2 = 0 + 16.33333333

Reorder the terms:
-16.33333333 + 16.33333333 + -0.6666666667x + x2 = 0 + 16.33333333

Combine like terms: -16.33333333 + 16.33333333 = 0.00000000
0.00000000 + -0.6666666667x + x2 = 0 + 16.33333333
-0.6666666667x + x2 = 0 + 16.33333333

Combine like terms: 0 + 16.33333333 = 16.33333333
-0.6666666667x + x2 = 16.33333333

The x term is -0.6666666667x.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667x + 0.1111111112 + x2 = 16.33333333 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667x + x2 = 16.33333333 + 0.1111111112

Combine like terms: 16.33333333 + 0.1111111112 = 16.4444444412
0.1111111112 + -0.6666666667x + x2 = 16.4444444412

Factor a perfect square on the left side:
(x + -0.3333333334)(x + -0.3333333334) = 16.4444444412

Calculate the square root of the right side: 4.05517502

Break this problem into two subproblems by setting 
(x + -0.3333333334) equal to 4.05517502 and -4.05517502.


Subproblem 1
x + -0.3333333334 = 4.05517502

Simplifying
x + -0.3333333334 = 4.05517502

Reorder the terms:
-0.3333333334 + x = 4.05517502

Solving
-0.3333333334 + x = 4.05517502

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = 4.05517502 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = 4.05517502 + 0.3333333334
x = 4.05517502 + 0.3333333334

Combine like terms: 4.05517502 + 0.3333333334 = 4.3885083534
x = 4.3885083534

Simplifying
x = 4.3885083534


Subproblem 2
x + -0.3333333334 = -4.05517502

Simplifying
x + -0.3333333334 = -4.05517502

Reorder the terms:
-0.3333333334 + x = -4.05517502

Solving
-0.3333333334 + x = -4.05517502

Solving for variable 'x'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + x = -4.05517502 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + x = -4.05517502 + 0.3333333334
x = -4.05517502 + 0.3333333334

Combine like terms: -4.05517502 + 0.3333333334 = -3.7218416866
x = -3.7218416866

Simplifying
x = -3.7218416866


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.3885083534, -3.7218416866}

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