3x^2-10x-8=10

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Solution for 3x^2-10x-8=10 equation: 


Simplifying
3x2 + -10x + -8 = 10

Reorder the terms:
-8 + -10x + 3x2 = 10

Solving
-8 + -10x + 3x2 = 10

Solving for variable 'x'.

Reorder the terms:
-8 + -10 + -10x + 3x2 = 10 + -10

Combine like terms: -8 + -10 = -18
-18 + -10x + 3x2 = 10 + -10

Combine like terms: 10 + -10 = 0
-18 + -10x + 3x2 = 0

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

Divide each side by '3'.
-6 + -3.333333333x + x2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + -3.333333333x + 6 + x2 = 0 + 6

Reorder the terms:
-6 + 6 + -3.333333333x + x2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -3.333333333x + x2 = 0 + 6
-3.333333333x + x2 = 0 + 6

Combine like terms: 0 + 6 = 6
-3.333333333x + x2 = 6

The x term is -3.333333333x.  Take half its coefficient (-1.666666667).
Square it (2.777777779) and add it to both sides.

Add '2.777777779' to each side of the equation.
-3.333333333x + 2.777777779 + x2 = 6 + 2.777777779

Reorder the terms:
2.777777779 + -3.333333333x + x2 = 6 + 2.777777779

Combine like terms: 6 + 2.777777779 = 8.777777779
2.777777779 + -3.333333333x + x2 = 8.777777779

Factor a perfect square on the left side:
(x + -1.666666667)(x + -1.666666667) = 8.777777779

Calculate the square root of the right side: 2.962731473

Break this problem into two subproblems by setting 
(x + -1.666666667) equal to 2.962731473 and -2.962731473.


Subproblem 1
x + -1.666666667 = 2.962731473

Simplifying
x + -1.666666667 = 2.962731473

Reorder the terms:
-1.666666667 + x = 2.962731473

Solving
-1.666666667 + x = 2.962731473

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = 2.962731473 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = 2.962731473 + 1.666666667
x = 2.962731473 + 1.666666667

Combine like terms: 2.962731473 + 1.666666667 = 4.62939814
x = 4.62939814

Simplifying
x = 4.62939814


Subproblem 2
x + -1.666666667 = -2.962731473

Simplifying
x + -1.666666667 = -2.962731473

Reorder the terms:
-1.666666667 + x = -2.962731473

Solving
-1.666666667 + x = -2.962731473

Solving for variable 'x'.

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

Add '1.666666667' to each side of the equation.
-1.666666667 + 1.666666667 + x = -2.962731473 + 1.666666667

Combine like terms: -1.666666667 + 1.666666667 = 0.000000000
0.000000000 + x = -2.962731473 + 1.666666667
x = -2.962731473 + 1.666666667

Combine like terms: -2.962731473 + 1.666666667 = -1.296064806
x = -1.296064806

Simplifying
x = -1.296064806


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.62939814, -1.296064806}

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