9x^2-43x-114=0

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Solution for 9x^2-43x-114=0 equation: 


Simplifying
9x2 + -43x + -114 = 0

Reorder the terms:
-114 + -43x + 9x2 = 0

Solving
-114 + -43x + 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'.
-12.66666667 + -4.777777778x + x2 = 0

Move the constant term to the right:

Add '12.66666667' to each side of the equation.
-12.66666667 + -4.777777778x + 12.66666667 + x2 = 0 + 12.66666667

Reorder the terms:
-12.66666667 + 12.66666667 + -4.777777778x + x2 = 0 + 12.66666667

Combine like terms: -12.66666667 + 12.66666667 = 0.00000000
0.00000000 + -4.777777778x + x2 = 0 + 12.66666667
-4.777777778x + x2 = 0 + 12.66666667

Combine like terms: 0 + 12.66666667 = 12.66666667
-4.777777778x + x2 = 12.66666667

The x term is -4.777777778x.  Take half its coefficient (-2.388888889).
Square it (5.706790124) and add it to both sides.

Add '5.706790124' to each side of the equation.
-4.777777778x + 5.706790124 + x2 = 12.66666667 + 5.706790124

Reorder the terms:
5.706790124 + -4.777777778x + x2 = 12.66666667 + 5.706790124

Combine like terms: 12.66666667 + 5.706790124 = 18.373456794
5.706790124 + -4.777777778x + x2 = 18.373456794

Factor a perfect square on the left side:
(x + -2.388888889)(x + -2.388888889) = 18.373456794

Calculate the square root of the right side: 4.286427043

Break this problem into two subproblems by setting 
(x + -2.388888889) equal to 4.286427043 and -4.286427043.


Subproblem 1
x + -2.388888889 = 4.286427043

Simplifying
x + -2.388888889 = 4.286427043

Reorder the terms:
-2.388888889 + x = 4.286427043

Solving
-2.388888889 + x = 4.286427043

Solving for variable 'x'.

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

Add '2.388888889' to each side of the equation.
-2.388888889 + 2.388888889 + x = 4.286427043 + 2.388888889

Combine like terms: -2.388888889 + 2.388888889 = 0.000000000
0.000000000 + x = 4.286427043 + 2.388888889
x = 4.286427043 + 2.388888889

Combine like terms: 4.286427043 + 2.388888889 = 6.675315932
x = 6.675315932

Simplifying
x = 6.675315932


Subproblem 2
x + -2.388888889 = -4.286427043

Simplifying
x + -2.388888889 = -4.286427043

Reorder the terms:
-2.388888889 + x = -4.286427043

Solving
-2.388888889 + x = -4.286427043

Solving for variable 'x'.

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

Add '2.388888889' to each side of the equation.
-2.388888889 + 2.388888889 + x = -4.286427043 + 2.388888889

Combine like terms: -2.388888889 + 2.388888889 = 0.000000000
0.000000000 + x = -4.286427043 + 2.388888889
x = -4.286427043 + 2.388888889

Combine like terms: -4.286427043 + 2.388888889 = -1.897538154
x = -1.897538154

Simplifying
x = -1.897538154


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.675315932, -1.897538154}

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