8x^2+22x-5=0

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Solution for 8x^2+22x-5=0 equation: 


Simplifying
8x2 + 22x + -5 = 0

Reorder the terms:
-5 + 22x + 8x2 = 0

Solving
-5 + 22x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
-0.625 + 2.75x + x2 = 0

Move the constant term to the right:

Add '0.625' to each side of the equation.
-0.625 + 2.75x + 0.625 + x2 = 0 + 0.625

Reorder the terms:
-0.625 + 0.625 + 2.75x + x2 = 0 + 0.625

Combine like terms: -0.625 + 0.625 = 0.000
0.000 + 2.75x + x2 = 0 + 0.625
2.75x + x2 = 0 + 0.625

Combine like terms: 0 + 0.625 = 0.625
2.75x + x2 = 0.625

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 = 0.625 + 1.890625

Reorder the terms:
1.890625 + 2.75x + x2 = 0.625 + 1.890625

Combine like terms: 0.625 + 1.890625 = 2.515625
1.890625 + 2.75x + x2 = 2.515625

Factor a perfect square on the left side:
(x + 1.375)(x + 1.375) = 2.515625

Calculate the square root of the right side: 1.586072193

Break this problem into two subproblems by setting 
(x + 1.375) equal to 1.586072193 and -1.586072193.


Subproblem 1
x + 1.375 = 1.586072193

Simplifying
x + 1.375 = 1.586072193

Reorder the terms:
1.375 + x = 1.586072193

Solving
1.375 + x = 1.586072193

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 = 1.586072193 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = 1.586072193 + -1.375
x = 1.586072193 + -1.375

Combine like terms: 1.586072193 + -1.375 = 0.211072193
x = 0.211072193

Simplifying
x = 0.211072193


Subproblem 2
x + 1.375 = -1.586072193

Simplifying
x + 1.375 = -1.586072193

Reorder the terms:
1.375 + x = -1.586072193

Solving
1.375 + x = -1.586072193

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 = -1.586072193 + -1.375

Combine like terms: 1.375 + -1.375 = 0.000
0.000 + x = -1.586072193 + -1.375
x = -1.586072193 + -1.375

Combine like terms: -1.586072193 + -1.375 = -2.961072193
x = -2.961072193

Simplifying
x = -2.961072193


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.211072193, -2.961072193}

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