56x^2+155x+71=-5x+7

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Solution for 56x^2+155x+71=-5x+7 equation: 


Simplifying
56x2 + 155x + 71 = -5x + 7

Reorder the terms:
71 + 155x + 56x2 = -5x + 7

Reorder the terms:
71 + 155x + 56x2 = 7 + -5x

Solving
71 + 155x + 56x2 = 7 + -5x

Solving for variable 'x'.

Reorder the terms:
71 + -7 + 155x + 5x + 56x2 = 7 + -5x + -7 + 5x

Combine like terms: 71 + -7 = 64
64 + 155x + 5x + 56x2 = 7 + -5x + -7 + 5x

Combine like terms: 155x + 5x = 160x
64 + 160x + 56x2 = 7 + -5x + -7 + 5x

Reorder the terms:
64 + 160x + 56x2 = 7 + -7 + -5x + 5x

Combine like terms: 7 + -7 = 0
64 + 160x + 56x2 = 0 + -5x + 5x
64 + 160x + 56x2 = -5x + 5x

Combine like terms: -5x + 5x = 0
64 + 160x + 56x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(8 + 20x + 7x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(8 + 20x + 7x2)' equal to zero and attempt to solve:

Simplifying
8 + 20x + 7x2 = 0

Solving
8 + 20x + 7x2 = 0

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

Divide each side by '7'.
1.142857143 + 2.857142857x + x2 = 0

Move the constant term to the right:

Add '-1.142857143' to each side of the equation.
1.142857143 + 2.857142857x + -1.142857143 + x2 = 0 + -1.142857143

Reorder the terms:
1.142857143 + -1.142857143 + 2.857142857x + x2 = 0 + -1.142857143

Combine like terms: 1.142857143 + -1.142857143 = 0.000000000
0.000000000 + 2.857142857x + x2 = 0 + -1.142857143
2.857142857x + x2 = 0 + -1.142857143

Combine like terms: 0 + -1.142857143 = -1.142857143
2.857142857x + x2 = -1.142857143

The x term is 2.857142857x.  Take half its coefficient (1.428571429).
Square it (2.040816328) and add it to both sides.

Add '2.040816328' to each side of the equation.
2.857142857x + 2.040816328 + x2 = -1.142857143 + 2.040816328

Reorder the terms:
2.040816328 + 2.857142857x + x2 = -1.142857143 + 2.040816328

Combine like terms: -1.142857143 + 2.040816328 = 0.897959185
2.040816328 + 2.857142857x + x2 = 0.897959185

Factor a perfect square on the left side:
(x + 1.428571429)(x + 1.428571429) = 0.897959185

Calculate the square root of the right side: 0.947607084

Break this problem into two subproblems by setting 
(x + 1.428571429) equal to 0.947607084 and -0.947607084.


Subproblem 1
x + 1.428571429 = 0.947607084

Simplifying
x + 1.428571429 = 0.947607084

Reorder the terms:
1.428571429 + x = 0.947607084

Solving
1.428571429 + x = 0.947607084

Solving for variable 'x'.

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

Add '-1.428571429' to each side of the equation.
1.428571429 + -1.428571429 + x = 0.947607084 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + x = 0.947607084 + -1.428571429
x = 0.947607084 + -1.428571429

Combine like terms: 0.947607084 + -1.428571429 = -0.480964345
x = -0.480964345

Simplifying
x = -0.480964345


Subproblem 2
x + 1.428571429 = -0.947607084

Simplifying
x + 1.428571429 = -0.947607084

Reorder the terms:
1.428571429 + x = -0.947607084

Solving
1.428571429 + x = -0.947607084

Solving for variable 'x'.

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

Add '-1.428571429' to each side of the equation.
1.428571429 + -1.428571429 + x = -0.947607084 + -1.428571429

Combine like terms: 1.428571429 + -1.428571429 = 0.000000000
0.000000000 + x = -0.947607084 + -1.428571429
x = -0.947607084 + -1.428571429

Combine like terms: -0.947607084 + -1.428571429 = -2.376178513
x = -2.376178513

Simplifying
x = -2.376178513


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.480964345, -2.376178513}
Solution
x = {-0.480964345, -2.376178513}

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