8x^2+26x+14=0

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Solution for 8x^2+26x+14=0 equation: 


Simplifying
8x2 + 26x + 14 = 0

Reorder the terms:
14 + 26x + 8x2 = 0

Solving
14 + 26x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(7 + 13x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(7 + 13x + 4x2)' equal to zero and attempt to solve:

Simplifying
7 + 13x + 4x2 = 0

Solving
7 + 13x + 4x2 = 0

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

Divide each side by '4'.
1.75 + 3.25x + x2 = 0

Move the constant term to the right:

Add '-1.75' to each side of the equation.
1.75 + 3.25x + -1.75 + x2 = 0 + -1.75

Reorder the terms:
1.75 + -1.75 + 3.25x + x2 = 0 + -1.75

Combine like terms: 1.75 + -1.75 = 0.00
0.00 + 3.25x + x2 = 0 + -1.75
3.25x + x2 = 0 + -1.75

Combine like terms: 0 + -1.75 = -1.75
3.25x + x2 = -1.75

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = -1.75 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = -1.75 + 2.640625

Combine like terms: -1.75 + 2.640625 = 0.890625
2.640625 + 3.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + 1.625) equal to 0.943729304 and -0.943729304.


Subproblem 1
x + 1.625 = 0.943729304

Simplifying
x + 1.625 = 0.943729304

Reorder the terms:
1.625 + x = 0.943729304

Solving
1.625 + x = 0.943729304

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = 0.943729304 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = 0.943729304 + -1.625
x = 0.943729304 + -1.625

Combine like terms: 0.943729304 + -1.625 = -0.681270696
x = -0.681270696

Simplifying
x = -0.681270696


Subproblem 2
x + 1.625 = -0.943729304

Simplifying
x + 1.625 = -0.943729304

Reorder the terms:
1.625 + x = -0.943729304

Solving
1.625 + x = -0.943729304

Solving for variable 'x'.

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

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = -0.943729304 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = -0.943729304 + -1.625
x = -0.943729304 + -1.625

Combine like terms: -0.943729304 + -1.625 = -2.568729304
x = -2.568729304

Simplifying
x = -2.568729304


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.681270696, -2.568729304}
Solution
x = {-0.681270696, -2.568729304}

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