3x^2+20x-22=0

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Solution for 3x^2+20x-22=0 equation: 


Simplifying
3x2 + 20x + -22 = 0

Reorder the terms:
-22 + 20x + 3x2 = 0

Solving
-22 + 20x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-7.333333333 + 6.666666667x + x2 = 0

Move the constant term to the right:

Add '7.333333333' to each side of the equation.
-7.333333333 + 6.666666667x + 7.333333333 + x2 = 0 + 7.333333333

Reorder the terms:
-7.333333333 + 7.333333333 + 6.666666667x + x2 = 0 + 7.333333333

Combine like terms: -7.333333333 + 7.333333333 = 0.000000000
0.000000000 + 6.666666667x + x2 = 0 + 7.333333333
6.666666667x + x2 = 0 + 7.333333333

Combine like terms: 0 + 7.333333333 = 7.333333333
6.666666667x + x2 = 7.333333333

The x term is 6.666666667x.  Take half its coefficient (3.333333334).
Square it (11.11111112) and add it to both sides.

Add '11.11111112' to each side of the equation.
6.666666667x + 11.11111112 + x2 = 7.333333333 + 11.11111112

Reorder the terms:
11.11111112 + 6.666666667x + x2 = 7.333333333 + 11.11111112

Combine like terms: 7.333333333 + 11.11111112 = 18.444444453
11.11111112 + 6.666666667x + x2 = 18.444444453

Factor a perfect square on the left side:
(x + 3.333333334)(x + 3.333333334) = 18.444444453

Calculate the square root of the right side: 4.294699577

Break this problem into two subproblems by setting 
(x + 3.333333334) equal to 4.294699577 and -4.294699577.


Subproblem 1
x + 3.333333334 = 4.294699577

Simplifying
x + 3.333333334 = 4.294699577

Reorder the terms:
3.333333334 + x = 4.294699577

Solving
3.333333334 + x = 4.294699577

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = 4.294699577 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = 4.294699577 + -3.333333334
x = 4.294699577 + -3.333333334

Combine like terms: 4.294699577 + -3.333333334 = 0.961366243
x = 0.961366243

Simplifying
x = 0.961366243


Subproblem 2
x + 3.333333334 = -4.294699577

Simplifying
x + 3.333333334 = -4.294699577

Reorder the terms:
3.333333334 + x = -4.294699577

Solving
3.333333334 + x = -4.294699577

Solving for variable 'x'.

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

Add '-3.333333334' to each side of the equation.
3.333333334 + -3.333333334 + x = -4.294699577 + -3.333333334

Combine like terms: 3.333333334 + -3.333333334 = 0.000000000
0.000000000 + x = -4.294699577 + -3.333333334
x = -4.294699577 + -3.333333334

Combine like terms: -4.294699577 + -3.333333334 = -7.628032911
x = -7.628032911

Simplifying
x = -7.628032911


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.961366243, -7.628032911}

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