26x^2+260x+620=0

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Solution for 26x^2+260x+620=0 equation: 


Simplifying
26x2 + 260x + 620 = 0

Reorder the terms:
620 + 260x + 26x2 = 0

Solving
620 + 260x + 26x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(310 + 130x + 13x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(310 + 130x + 13x2)' equal to zero and attempt to solve:

Simplifying
310 + 130x + 13x2 = 0

Solving
310 + 130x + 13x2 = 0

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

Divide each side by '13'.
23.84615385 + 10x + x2 = 0

Move the constant term to the right:

Add '-23.84615385' to each side of the equation.
23.84615385 + 10x + -23.84615385 + x2 = 0 + -23.84615385

Reorder the terms:
23.84615385 + -23.84615385 + 10x + x2 = 0 + -23.84615385

Combine like terms: 23.84615385 + -23.84615385 = 0.00000000
0.00000000 + 10x + x2 = 0 + -23.84615385
10x + x2 = 0 + -23.84615385

Combine like terms: 0 + -23.84615385 = -23.84615385
10x + x2 = -23.84615385

The x term is 10x.  Take half its coefficient (5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
10x + 25 + x2 = -23.84615385 + 25

Reorder the terms:
25 + 10x + x2 = -23.84615385 + 25

Combine like terms: -23.84615385 + 25 = 1.15384615
25 + 10x + x2 = 1.15384615

Factor a perfect square on the left side:
(x + 5)(x + 5) = 1.15384615

Calculate the square root of the right side: 1.074172309

Break this problem into two subproblems by setting 
(x + 5) equal to 1.074172309 and -1.074172309.


Subproblem 1
x + 5 = 1.074172309

Simplifying
x + 5 = 1.074172309

Reorder the terms:
5 + x = 1.074172309

Solving
5 + x = 1.074172309

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = 1.074172309 + -5

Combine like terms: 5 + -5 = 0
0 + x = 1.074172309 + -5
x = 1.074172309 + -5

Combine like terms: 1.074172309 + -5 = -3.925827691
x = -3.925827691

Simplifying
x = -3.925827691


Subproblem 2
x + 5 = -1.074172309

Simplifying
x + 5 = -1.074172309

Reorder the terms:
5 + x = -1.074172309

Solving
5 + x = -1.074172309

Solving for variable 'x'.

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

Add '-5' to each side of the equation.
5 + -5 + x = -1.074172309 + -5

Combine like terms: 5 + -5 = 0
0 + x = -1.074172309 + -5
x = -1.074172309 + -5

Combine like terms: -1.074172309 + -5 = -6.074172309
x = -6.074172309

Simplifying
x = -6.074172309


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.925827691, -6.074172309}
Solution
x = {-3.925827691, -6.074172309}

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