3x^2-29x-56=0

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Solution for 3x^2-29x-56=0 equation: 


Simplifying
3x2 + -29x + -56 = 0

Reorder the terms:
-56 + -29x + 3x2 = 0

Solving
-56 + -29x + 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'.
-18.66666667 + -9.666666667x + x2 = 0

Move the constant term to the right:

Add '18.66666667' to each side of the equation.
-18.66666667 + -9.666666667x + 18.66666667 + x2 = 0 + 18.66666667

Reorder the terms:
-18.66666667 + 18.66666667 + -9.666666667x + x2 = 0 + 18.66666667

Combine like terms: -18.66666667 + 18.66666667 = 0.00000000
0.00000000 + -9.666666667x + x2 = 0 + 18.66666667
-9.666666667x + x2 = 0 + 18.66666667

Combine like terms: 0 + 18.66666667 = 18.66666667
-9.666666667x + x2 = 18.66666667

The x term is -9.666666667x.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667x + 23.36111112 + x2 = 18.66666667 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667x + x2 = 18.66666667 + 23.36111112

Combine like terms: 18.66666667 + 23.36111112 = 42.02777779
23.36111112 + -9.666666667x + x2 = 42.02777779

Factor a perfect square on the left side:
(x + -4.833333334)(x + -4.833333334) = 42.02777779

Calculate the square root of the right side: 6.482883447

Break this problem into two subproblems by setting 
(x + -4.833333334) equal to 6.482883447 and -6.482883447.


Subproblem 1
x + -4.833333334 = 6.482883447

Simplifying
x + -4.833333334 = 6.482883447

Reorder the terms:
-4.833333334 + x = 6.482883447

Solving
-4.833333334 + x = 6.482883447

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = 6.482883447 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = 6.482883447 + 4.833333334
x = 6.482883447 + 4.833333334

Combine like terms: 6.482883447 + 4.833333334 = 11.316216781
x = 11.316216781

Simplifying
x = 11.316216781


Subproblem 2
x + -4.833333334 = -6.482883447

Simplifying
x + -4.833333334 = -6.482883447

Reorder the terms:
-4.833333334 + x = -6.482883447

Solving
-4.833333334 + x = -6.482883447

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = -6.482883447 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = -6.482883447 + 4.833333334
x = -6.482883447 + 4.833333334

Combine like terms: -6.482883447 + 4.833333334 = -1.649550113
x = -1.649550113

Simplifying
x = -1.649550113


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {11.316216781, -1.649550113}

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