-3x^2+56x+29=0

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


Simplifying
-3x2 + 56x + 29 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: -9.666666667 + 9.666666667 = 0.000000000
0.000000000 + -18.66666667x + x2 = 0 + 9.666666667
-18.66666667x + x2 = 0 + 9.666666667

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

The x term is -18.66666667x.  Take half its coefficient (-9.333333335).
Square it (87.11111114) and add it to both sides.

Add '87.11111114' to each side of the equation.
-18.66666667x + 87.11111114 + x2 = 9.666666667 + 87.11111114

Reorder the terms:
87.11111114 + -18.66666667x + x2 = 9.666666667 + 87.11111114

Combine like terms: 9.666666667 + 87.11111114 = 96.777777807
87.11111114 + -18.66666667x + x2 = 96.777777807

Factor a perfect square on the left side:
(x + -9.333333335)(x + -9.333333335) = 96.777777807

Calculate the square root of the right side: 9.83756971

Break this problem into two subproblems by setting 
(x + -9.333333335) equal to 9.83756971 and -9.83756971.


Subproblem 1
x + -9.333333335 = 9.83756971

Simplifying
x + -9.333333335 = 9.83756971

Reorder the terms:
-9.333333335 + x = 9.83756971

Solving
-9.333333335 + x = 9.83756971

Solving for variable 'x'.

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

Add '9.333333335' to each side of the equation.
-9.333333335 + 9.333333335 + x = 9.83756971 + 9.333333335

Combine like terms: -9.333333335 + 9.333333335 = 0.000000000
0.000000000 + x = 9.83756971 + 9.333333335
x = 9.83756971 + 9.333333335

Combine like terms: 9.83756971 + 9.333333335 = 19.170903045
x = 19.170903045

Simplifying
x = 19.170903045


Subproblem 2
x + -9.333333335 = -9.83756971

Simplifying
x + -9.333333335 = -9.83756971

Reorder the terms:
-9.333333335 + x = -9.83756971

Solving
-9.333333335 + x = -9.83756971

Solving for variable 'x'.

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

Add '9.333333335' to each side of the equation.
-9.333333335 + 9.333333335 + x = -9.83756971 + 9.333333335

Combine like terms: -9.333333335 + 9.333333335 = 0.000000000
0.000000000 + x = -9.83756971 + 9.333333335
x = -9.83756971 + 9.333333335

Combine like terms: -9.83756971 + 9.333333335 = -0.504236375
x = -0.504236375

Simplifying
x = -0.504236375


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {19.170903045, -0.504236375}

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