x^2+140x+183=0

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Solution for x^2+140x+183=0 equation: 


Simplifying
x2 + 140x + 183 = 0

Reorder the terms:
183 + 140x + x2 = 0

Solving
183 + 140x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-183' to each side of the equation.
183 + 140x + -183 + x2 = 0 + -183

Reorder the terms:
183 + -183 + 140x + x2 = 0 + -183

Combine like terms: 183 + -183 = 0
0 + 140x + x2 = 0 + -183
140x + x2 = 0 + -183

Combine like terms: 0 + -183 = -183
140x + x2 = -183

The x term is 140x.  Take half its coefficient (70).
Square it (4900) and add it to both sides.

Add '4900' to each side of the equation.
140x + 4900 + x2 = -183 + 4900

Reorder the terms:
4900 + 140x + x2 = -183 + 4900

Combine like terms: -183 + 4900 = 4717
4900 + 140x + x2 = 4717

Factor a perfect square on the left side:
(x + 70)(x + 70) = 4717

Calculate the square root of the right side: 68.680419335

Break this problem into two subproblems by setting 
(x + 70) equal to 68.680419335 and -68.680419335.


Subproblem 1
x + 70 = 68.680419335

Simplifying
x + 70 = 68.680419335

Reorder the terms:
70 + x = 68.680419335

Solving
70 + x = 68.680419335

Solving for variable 'x'.

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

Add '-70' to each side of the equation.
70 + -70 + x = 68.680419335 + -70

Combine like terms: 70 + -70 = 0
0 + x = 68.680419335 + -70
x = 68.680419335 + -70

Combine like terms: 68.680419335 + -70 = -1.319580665
x = -1.319580665

Simplifying
x = -1.319580665


Subproblem 2
x + 70 = -68.680419335

Simplifying
x + 70 = -68.680419335

Reorder the terms:
70 + x = -68.680419335

Solving
70 + x = -68.680419335

Solving for variable 'x'.

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

Add '-70' to each side of the equation.
70 + -70 + x = -68.680419335 + -70

Combine like terms: 70 + -70 = 0
0 + x = -68.680419335 + -70
x = -68.680419335 + -70

Combine like terms: -68.680419335 + -70 = -138.680419335
x = -138.680419335

Simplifying
x = -138.680419335


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.319580665, -138.680419335}

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