6x^2+59x=-56

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Solution for 6x^2+59x=-56 equation: 


Simplifying
6x2 + 59x = -56

Reorder the terms:
59x + 6x2 = -56

Solving
59x + 6x2 = -56

Solving for variable 'x'.

Reorder the terms:
56 + 59x + 6x2 = -56 + 56

Combine like terms: -56 + 56 = 0
56 + 59x + 6x2 = 0

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

Divide each side by '6'.
9.333333333 + 9.833333333x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + 9.833333333x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + 9.833333333x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + 9.833333333x + x2 = 0 + -9.333333333
9.833333333x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
9.833333333x + x2 = -9.333333333

The x term is 9.833333333x.  Take half its coefficient (4.916666667).
Square it (24.17361111) and add it to both sides.

Add '24.17361111' to each side of the equation.
9.833333333x + 24.17361111 + x2 = -9.333333333 + 24.17361111

Reorder the terms:
24.17361111 + 9.833333333x + x2 = -9.333333333 + 24.17361111

Combine like terms: -9.333333333 + 24.17361111 = 14.840277777
24.17361111 + 9.833333333x + x2 = 14.840277777

Factor a perfect square on the left side:
(x + 4.916666667)(x + 4.916666667) = 14.840277777

Calculate the square root of the right side: 3.85230811

Break this problem into two subproblems by setting 
(x + 4.916666667) equal to 3.85230811 and -3.85230811.


Subproblem 1
x + 4.916666667 = 3.85230811

Simplifying
x + 4.916666667 = 3.85230811

Reorder the terms:
4.916666667 + x = 3.85230811

Solving
4.916666667 + x = 3.85230811

Solving for variable 'x'.

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

Add '-4.916666667' to each side of the equation.
4.916666667 + -4.916666667 + x = 3.85230811 + -4.916666667

Combine like terms: 4.916666667 + -4.916666667 = 0.000000000
0.000000000 + x = 3.85230811 + -4.916666667
x = 3.85230811 + -4.916666667

Combine like terms: 3.85230811 + -4.916666667 = -1.064358557
x = -1.064358557

Simplifying
x = -1.064358557


Subproblem 2
x + 4.916666667 = -3.85230811

Simplifying
x + 4.916666667 = -3.85230811

Reorder the terms:
4.916666667 + x = -3.85230811

Solving
4.916666667 + x = -3.85230811

Solving for variable 'x'.

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

Add '-4.916666667' to each side of the equation.
4.916666667 + -4.916666667 + x = -3.85230811 + -4.916666667

Combine like terms: 4.916666667 + -4.916666667 = 0.000000000
0.000000000 + x = -3.85230811 + -4.916666667
x = -3.85230811 + -4.916666667

Combine like terms: -3.85230811 + -4.916666667 = -8.768974777
x = -8.768974777

Simplifying
x = -8.768974777


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.064358557, -8.768974777}

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