5x^2+8x-22=0

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


Simplifying
5x2 + 8x + -22 = 0

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

Solving
-22 + 8x + 5x2 = 0

Solving for variable 'x'.

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

Divide each side by '5'.
-4.4 + 1.6x + x2 = 0

Move the constant term to the right:

Add '4.4' to each side of the equation.
-4.4 + 1.6x + 4.4 + x2 = 0 + 4.4

Reorder the terms:
-4.4 + 4.4 + 1.6x + x2 = 0 + 4.4

Combine like terms: -4.4 + 4.4 = 0.0
0.0 + 1.6x + x2 = 0 + 4.4
1.6x + x2 = 0 + 4.4

Combine like terms: 0 + 4.4 = 4.4
1.6x + x2 = 4.4

The x term is 1.6x.  Take half its coefficient (0.8).
Square it (0.64) and add it to both sides.

Add '0.64' to each side of the equation.
1.6x + 0.64 + x2 = 4.4 + 0.64

Reorder the terms:
0.64 + 1.6x + x2 = 4.4 + 0.64

Combine like terms: 4.4 + 0.64 = 5.04
0.64 + 1.6x + x2 = 5.04

Factor a perfect square on the left side:
(x + 0.8)(x + 0.8) = 5.04

Calculate the square root of the right side: 2.244994432

Break this problem into two subproblems by setting 
(x + 0.8) equal to 2.244994432 and -2.244994432.


Subproblem 1
x + 0.8 = 2.244994432

Simplifying
x + 0.8 = 2.244994432

Reorder the terms:
0.8 + x = 2.244994432

Solving
0.8 + x = 2.244994432

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = 2.244994432 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = 2.244994432 + -0.8
x = 2.244994432 + -0.8

Combine like terms: 2.244994432 + -0.8 = 1.444994432
x = 1.444994432

Simplifying
x = 1.444994432


Subproblem 2
x + 0.8 = -2.244994432

Simplifying
x + 0.8 = -2.244994432

Reorder the terms:
0.8 + x = -2.244994432

Solving
0.8 + x = -2.244994432

Solving for variable 'x'.

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

Add '-0.8' to each side of the equation.
0.8 + -0.8 + x = -2.244994432 + -0.8

Combine like terms: 0.8 + -0.8 = 0.0
0.0 + x = -2.244994432 + -0.8
x = -2.244994432 + -0.8

Combine like terms: -2.244994432 + -0.8 = -3.044994432
x = -3.044994432

Simplifying
x = -3.044994432


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.444994432, -3.044994432}

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