8x^2+22x-20=0

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Solution for 8x^2+22x-20=0 equation: 


Simplifying
8x2 + 22x + -20 = 0

Reorder the terms:
-20 + 22x + 8x2 = 0

Solving
-20 + 22x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-10 + 11x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-10 + 11x + 4x2)' equal to zero and attempt to solve:

Simplifying
-10 + 11x + 4x2 = 0

Solving
-10 + 11x + 4x2 = 0

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

Divide each side by '4'.
-2.5 + 2.75x + x2 = 0

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + 2.75x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + 2.75x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 2.75x + x2 = 0 + 2.5
2.75x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
2.75x + x2 = 2.5

The x term is 2.75x.  Take half its coefficient (1.375).
Square it (1.890625) and add it to both sides.

Add '1.890625' to each side of the equation.
2.75x + 1.890625 + x2 = 2.5 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = 2.5 + 1.890625

Combine like terms: 2.5 + 1.890625 = 4.390625
1.890625 + 2.75x + x2 = 4.390625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 4.390625

Calculate the square root of the right side: 2.095381827

Break this problem into two subproblems by setting 
(x + 1.375) equal to 2.095381827 and -2.095381827.


Subproblem 1
x + 1.375 = 2.095381827

Simplifying
x + 1.375 = 2.095381827

Reorder the terms:
1.375 + x = 2.095381827

Solving
1.375 + x = 2.095381827

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = 2.095381827 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = 2.095381827 + -1.375
x = 2.095381827 + -1.375

Combine like terms: 2.095381827 + -1.375 = 0.720381827
x = 0.720381827

Simplifying
x = 0.720381827


Subproblem 2
x + 1.375 = -2.095381827

Simplifying
x + 1.375 = -2.095381827

Reorder the terms:
1.375 + x = -2.095381827

Solving
1.375 + x = -2.095381827

Solving for variable 'x'.

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

Add '-1.375' to each side of the equation.
1.375 + -1.375 + x = -2.095381827 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = -2.095381827 + -1.375
x = -2.095381827 + -1.375

Combine like terms: -2.095381827 + -1.375 = -3.470381827
x = -3.470381827

Simplifying
x = -3.470381827


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.720381827, -3.470381827}
Solution
x = {0.720381827, -3.470381827}

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