3x^2+10x-8=121

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Solution for 3x^2+10x-8=121 equation: 


Simplifying
3x2 + 10x + -8 = 121

Reorder the terms:
-8 + 10x + 3x2 = 121

Solving
-8 + 10x + 3x2 = 121

Solving for variable 'x'.

Reorder the terms:
-8 + -121 + 10x + 3x2 = 121 + -121

Combine like terms: -8 + -121 = -129
-129 + 10x + 3x2 = 121 + -121

Combine like terms: 121 + -121 = 0
-129 + 10x + 3x2 = 0

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

Divide each side by '3'.
-43 + 3.333333333x + x2 = 0

Move the constant term to the right:

Add '43' to each side of the equation.
-43 + 3.333333333x + 43 + x2 = 0 + 43

Reorder the terms:
-43 + 43 + 3.333333333x + x2 = 0 + 43

Combine like terms: -43 + 43 = 0
0 + 3.333333333x + x2 = 0 + 43
3.333333333x + x2 = 0 + 43

Combine like terms: 0 + 43 = 43
3.333333333x + x2 = 43

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 = 43 + 2.777777779

Reorder the terms:
2.777777779 + 3.333333333x + x2 = 43 + 2.777777779

Combine like terms: 43 + 2.777777779 = 45.777777779
2.777777779 + 3.333333333x + x2 = 45.777777779

Factor a perfect square on the left side:
(x + 1.666666667)(x + 1.666666667) = 45.777777779

Calculate the square root of the right side: 6.76592771

Break this problem into two subproblems by setting 
(x + 1.666666667) equal to 6.76592771 and -6.76592771.


Subproblem 1
x + 1.666666667 = 6.76592771

Simplifying
x + 1.666666667 = 6.76592771

Reorder the terms:
1.666666667 + x = 6.76592771

Solving
1.666666667 + x = 6.76592771

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 = 6.76592771 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = 6.76592771 + -1.666666667
x = 6.76592771 + -1.666666667

Combine like terms: 6.76592771 + -1.666666667 = 5.099261043
x = 5.099261043

Simplifying
x = 5.099261043


Subproblem 2
x + 1.666666667 = -6.76592771

Simplifying
x + 1.666666667 = -6.76592771

Reorder the terms:
1.666666667 + x = -6.76592771

Solving
1.666666667 + x = -6.76592771

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 = -6.76592771 + -1.666666667

Combine like terms: 1.666666667 + -1.666666667 = 0.000000000
0.000000000 + x = -6.76592771 + -1.666666667
x = -6.76592771 + -1.666666667

Combine like terms: -6.76592771 + -1.666666667 = -8.432594377
x = -8.432594377

Simplifying
x = -8.432594377


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.099261043, -8.432594377}

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