20x^2+2x-68=0

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Solution for 20x^2+2x-68=0 equation: 


Simplifying
20x2 + 2x + -68 = 0

Reorder the terms:
-68 + 2x + 20x2 = 0

Solving
-68 + 2x + 20x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-34 + x + 10x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-34 + x + 10x2)' equal to zero and attempt to solve:

Simplifying
-34 + x + 10x2 = 0

Solving
-34 + x + 10x2 = 0

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

Divide each side by '10'.
-3.4 + 0.1x + x2 = 0.0

Move the constant term to the right:

Add '3.4' to each side of the equation.
-3.4 + 0.1x + 3.4 + x2 = 0.0 + 3.4

Reorder the terms:
-3.4 + 3.4 + 0.1x + x2 = 0.0 + 3.4

Combine like terms: -3.4 + 3.4 = 0.0
0.0 + 0.1x + x2 = 0.0 + 3.4
0.1x + x2 = 0.0 + 3.4

Combine like terms: 0.0 + 3.4 = 3.4
0.1x + x2 = 3.4

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.1x + 0.25 + x2 = 3.4 + 0.25

Reorder the terms:
0.25 + 0.1x + x2 = 3.4 + 0.25

Combine like terms: 3.4 + 0.25 = 3.65
0.25 + 0.1x + x2 = 3.65

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 3.65

Calculate the square root of the right side: 1.910497317

Break this problem into two subproblems by setting 
(x + 0.5) equal to 1.910497317 and -1.910497317.


Subproblem 1
x + 0.5 = 1.910497317

Simplifying
x + 0.5 = 1.910497317

Reorder the terms:
0.5 + x = 1.910497317

Solving
0.5 + x = 1.910497317

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 1.910497317 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 1.910497317 + -0.5
x = 1.910497317 + -0.5

Combine like terms: 1.910497317 + -0.5 = 1.410497317
x = 1.410497317

Simplifying
x = 1.410497317


Subproblem 2
x + 0.5 = -1.910497317

Simplifying
x + 0.5 = -1.910497317

Reorder the terms:
0.5 + x = -1.910497317

Solving
0.5 + x = -1.910497317

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -1.910497317 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -1.910497317 + -0.5
x = -1.910497317 + -0.5

Combine like terms: -1.910497317 + -0.5 = -2.410497317
x = -2.410497317

Simplifying
x = -2.410497317


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.410497317, -2.410497317}
Solution
x = {1.410497317, -2.410497317}

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