3x^2-13x-4=8-4

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Solution for 3x^2-13x-4=8-4 equation: 


Simplifying
3x2 + -13x + -4 = 8 + -4

Reorder the terms:
-4 + -13x + 3x2 = 8 + -4

Combine like terms: 8 + -4 = 4
-4 + -13x + 3x2 = 4

Solving
-4 + -13x + 3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-4 + -4 + -13x + 3x2 = 4 + -4

Combine like terms: -4 + -4 = -8
-8 + -13x + 3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-8 + -13x + 3x2 = 0

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

Divide each side by '3'.
-2.666666667 + -4.333333333x + x2 = 0

Move the constant term to the right:

Add '2.666666667' to each side of the equation.
-2.666666667 + -4.333333333x + 2.666666667 + x2 = 0 + 2.666666667

Reorder the terms:
-2.666666667 + 2.666666667 + -4.333333333x + x2 = 0 + 2.666666667

Combine like terms: -2.666666667 + 2.666666667 = 0.000000000
0.000000000 + -4.333333333x + x2 = 0 + 2.666666667
-4.333333333x + x2 = 0 + 2.666666667

Combine like terms: 0 + 2.666666667 = 2.666666667
-4.333333333x + x2 = 2.666666667

The x term is -4.333333333x.  Take half its coefficient (-2.166666667).
Square it (4.694444446) and add it to both sides.

Add '4.694444446' to each side of the equation.
-4.333333333x + 4.694444446 + x2 = 2.666666667 + 4.694444446

Reorder the terms:
4.694444446 + -4.333333333x + x2 = 2.666666667 + 4.694444446

Combine like terms: 2.666666667 + 4.694444446 = 7.361111113
4.694444446 + -4.333333333x + x2 = 7.361111113

Factor a perfect square on the left side:
(x + -2.166666667)(x + -2.166666667) = 7.361111113

Calculate the square root of the right side: 2.713136766

Break this problem into two subproblems by setting 
(x + -2.166666667) equal to 2.713136766 and -2.713136766.


Subproblem 1
x + -2.166666667 = 2.713136766

Simplifying
x + -2.166666667 = 2.713136766

Reorder the terms:
-2.166666667 + x = 2.713136766

Solving
-2.166666667 + x = 2.713136766

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = 2.713136766 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = 2.713136766 + 2.166666667
x = 2.713136766 + 2.166666667

Combine like terms: 2.713136766 + 2.166666667 = 4.879803433
x = 4.879803433

Simplifying
x = 4.879803433


Subproblem 2
x + -2.166666667 = -2.713136766

Simplifying
x + -2.166666667 = -2.713136766

Reorder the terms:
-2.166666667 + x = -2.713136766

Solving
-2.166666667 + x = -2.713136766

Solving for variable 'x'.

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

Add '2.166666667' to each side of the equation.
-2.166666667 + 2.166666667 + x = -2.713136766 + 2.166666667

Combine like terms: -2.166666667 + 2.166666667 = 0.000000000
0.000000000 + x = -2.713136766 + 2.166666667
x = -2.713136766 + 2.166666667

Combine like terms: -2.713136766 + 2.166666667 = -0.546470099
x = -0.546470099

Simplifying
x = -0.546470099


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.879803433, -0.546470099}

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