0=x^2+26x+140

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Solution for 0=x^2+26x+140 equation: 


Simplifying
0 = x2 + 26x + 140

Reorder the terms:
0 = 140 + 26x + x2

Solving
0 = 140 + 26x + x2

Solving for variable 'x'.

Combine like terms: 0 + -140 = -140
-140 + -26x + -1x2 = 140 + 26x + x2 + -140 + -26x + -1x2

Reorder the terms:
-140 + -26x + -1x2 = 140 + -140 + 26x + -26x + x2 + -1x2

Combine like terms: 140 + -140 = 0
-140 + -26x + -1x2 = 0 + 26x + -26x + x2 + -1x2
-140 + -26x + -1x2 = 26x + -26x + x2 + -1x2

Combine like terms: 26x + -26x = 0
-140 + -26x + -1x2 = 0 + x2 + -1x2
-140 + -26x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-140 + -26x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(140 + 26x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(140 + 26x + x2)' equal to zero and attempt to solve:

Simplifying
140 + 26x + x2 = 0

Solving
140 + 26x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-140' to each side of the equation.
140 + 26x + -140 + x2 = 0 + -140

Reorder the terms:
140 + -140 + 26x + x2 = 0 + -140

Combine like terms: 140 + -140 = 0
0 + 26x + x2 = 0 + -140
26x + x2 = 0 + -140

Combine like terms: 0 + -140 = -140
26x + x2 = -140

The x term is 26x.  Take half its coefficient (13).
Square it (169) and add it to both sides.

Add '169' to each side of the equation.
26x + 169 + x2 = -140 + 169

Reorder the terms:
169 + 26x + x2 = -140 + 169

Combine like terms: -140 + 169 = 29
169 + 26x + x2 = 29

Factor a perfect square on the left side:
(x + 13)(x + 13) = 29

Calculate the square root of the right side: 5.385164807

Break this problem into two subproblems by setting 
(x + 13) equal to 5.385164807 and -5.385164807.


Subproblem 1
x + 13 = 5.385164807

Simplifying
x + 13 = 5.385164807

Reorder the terms:
13 + x = 5.385164807

Solving
13 + x = 5.385164807

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + x = 5.385164807 + -13

Combine like terms: 13 + -13 = 0
0 + x = 5.385164807 + -13
x = 5.385164807 + -13

Combine like terms: 5.385164807 + -13 = -7.614835193
x = -7.614835193

Simplifying
x = -7.614835193


Subproblem 2
x + 13 = -5.385164807

Simplifying
x + 13 = -5.385164807

Reorder the terms:
13 + x = -5.385164807

Solving
13 + x = -5.385164807

Solving for variable 'x'.

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

Add '-13' to each side of the equation.
13 + -13 + x = -5.385164807 + -13

Combine like terms: 13 + -13 = 0
0 + x = -5.385164807 + -13
x = -5.385164807 + -13

Combine like terms: -5.385164807 + -13 = -18.385164807
x = -18.385164807

Simplifying
x = -18.385164807


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-7.614835193, -18.385164807}
Solution
x = {-7.614835193, -18.385164807}

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