9x^2-42x-8=0

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Solution for 9x^2-42x-8=0 equation: 


Simplifying
9x2 + -42x + -8 = 0

Reorder the terms:
-8 + -42x + 9x2 = 0

Solving
-8 + -42x + 9x2 = 0

Solving for variable 'x'.

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

Divide each side by '9'.
-0.8888888889 + -4.666666667x + x2 = 0

Move the constant term to the right:

Add '0.8888888889' to each side of the equation.
-0.8888888889 + -4.666666667x + 0.8888888889 + x2 = 0 + 0.8888888889

Reorder the terms:
-0.8888888889 + 0.8888888889 + -4.666666667x + x2 = 0 + 0.8888888889

Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000
0.0000000000 + -4.666666667x + x2 = 0 + 0.8888888889
-4.666666667x + x2 = 0 + 0.8888888889

Combine like terms: 0 + 0.8888888889 = 0.8888888889
-4.666666667x + x2 = 0.8888888889

The x term is -4.666666667x.  Take half its coefficient (-2.333333334).
Square it (5.444444448) and add it to both sides.

Add '5.444444448' to each side of the equation.
-4.666666667x + 5.444444448 + x2 = 0.8888888889 + 5.444444448

Reorder the terms:
5.444444448 + -4.666666667x + x2 = 0.8888888889 + 5.444444448

Combine like terms: 0.8888888889 + 5.444444448 = 6.3333333369
5.444444448 + -4.666666667x + x2 = 6.3333333369

Factor a perfect square on the left side:
(x + -2.333333334)(x + -2.333333334) = 6.3333333369

Calculate the square root of the right side: 2.516611479

Break this problem into two subproblems by setting 
(x + -2.333333334) equal to 2.516611479 and -2.516611479.


Subproblem 1
x + -2.333333334 = 2.516611479

Simplifying
x + -2.333333334 = 2.516611479

Reorder the terms:
-2.333333334 + x = 2.516611479

Solving
-2.333333334 + x = 2.516611479

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = 2.516611479 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = 2.516611479 + 2.333333334
x = 2.516611479 + 2.333333334

Combine like terms: 2.516611479 + 2.333333334 = 4.849944813
x = 4.849944813

Simplifying
x = 4.849944813


Subproblem 2
x + -2.333333334 = -2.516611479

Simplifying
x + -2.333333334 = -2.516611479

Reorder the terms:
-2.333333334 + x = -2.516611479

Solving
-2.333333334 + x = -2.516611479

Solving for variable 'x'.

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

Add '2.333333334' to each side of the equation.
-2.333333334 + 2.333333334 + x = -2.516611479 + 2.333333334

Combine like terms: -2.333333334 + 2.333333334 = 0.000000000
0.000000000 + x = -2.516611479 + 2.333333334
x = -2.516611479 + 2.333333334

Combine like terms: -2.516611479 + 2.333333334 = -0.183278145
x = -0.183278145

Simplifying
x = -0.183278145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.849944813, -0.183278145}

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