3x^2-22x-42=0

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Solution for 3x^2-22x-42=0 equation: 


Simplifying
3x2 + -22x + -42 = 0

Reorder the terms:
-42 + -22x + 3x2 = 0

Solving
-42 + -22x + 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'.
-14 + -7.333333333x + x2 = 0

Move the constant term to the right:

Add '14' to each side of the equation.
-14 + -7.333333333x + 14 + x2 = 0 + 14

Reorder the terms:
-14 + 14 + -7.333333333x + x2 = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -7.333333333x + x2 = 0 + 14
-7.333333333x + x2 = 0 + 14

Combine like terms: 0 + 14 = 14
-7.333333333x + x2 = 14

The x term is -7.333333333x.  Take half its coefficient (-3.666666667).
Square it (13.44444445) and add it to both sides.

Add '13.44444445' to each side of the equation.
-7.333333333x + 13.44444445 + x2 = 14 + 13.44444445

Reorder the terms:
13.44444445 + -7.333333333x + x2 = 14 + 13.44444445

Combine like terms: 14 + 13.44444445 = 27.44444445
13.44444445 + -7.333333333x + x2 = 27.44444445

Factor a perfect square on the left side:
(x + -3.666666667)(x + -3.666666667) = 27.44444445

Calculate the square root of the right side: 5.238744549

Break this problem into two subproblems by setting 
(x + -3.666666667) equal to 5.238744549 and -5.238744549.


Subproblem 1
x + -3.666666667 = 5.238744549

Simplifying
x + -3.666666667 = 5.238744549

Reorder the terms:
-3.666666667 + x = 5.238744549

Solving
-3.666666667 + x = 5.238744549

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = 5.238744549 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = 5.238744549 + 3.666666667
x = 5.238744549 + 3.666666667

Combine like terms: 5.238744549 + 3.666666667 = 8.905411216
x = 8.905411216

Simplifying
x = 8.905411216


Subproblem 2
x + -3.666666667 = -5.238744549

Simplifying
x + -3.666666667 = -5.238744549

Reorder the terms:
-3.666666667 + x = -5.238744549

Solving
-3.666666667 + x = -5.238744549

Solving for variable 'x'.

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

Add '3.666666667' to each side of the equation.
-3.666666667 + 3.666666667 + x = -5.238744549 + 3.666666667

Combine like terms: -3.666666667 + 3.666666667 = 0.000000000
0.000000000 + x = -5.238744549 + 3.666666667
x = -5.238744549 + 3.666666667

Combine like terms: -5.238744549 + 3.666666667 = -1.572077882
x = -1.572077882

Simplifying
x = -1.572077882


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.905411216, -1.572077882}

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