=9x^2-67x-116

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Solution for =9x^2-67x-116 equation:


Simplifying
0 = 9x2 + -67x + -116

Reorder the terms:
0 = -116 + -67x + 9x2

Solving
0 = -116 + -67x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + 116 = 116
116 + 67x + -9x2 = -116 + -67x + 9x2 + 116 + 67x + -9x2

Reorder the terms:
116 + 67x + -9x2 = -116 + 116 + -67x + 67x + 9x2 + -9x2

Combine like terms: -116 + 116 = 0
116 + 67x + -9x2 = 0 + -67x + 67x + 9x2 + -9x2
116 + 67x + -9x2 = -67x + 67x + 9x2 + -9x2

Combine like terms: -67x + 67x = 0
116 + 67x + -9x2 = 0 + 9x2 + -9x2
116 + 67x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
116 + 67x + -9x2 = 0

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

Divide each side by '-9'.
-12.88888889 + -7.444444444x + x2 = 0

Move the constant term to the right:

Add '12.88888889' to each side of the equation.
-12.88888889 + -7.444444444x + 12.88888889 + x2 = 0 + 12.88888889

Reorder the terms:
-12.88888889 + 12.88888889 + -7.444444444x + x2 = 0 + 12.88888889

Combine like terms: -12.88888889 + 12.88888889 = 0.00000000
0.00000000 + -7.444444444x + x2 = 0 + 12.88888889
-7.444444444x + x2 = 0 + 12.88888889

Combine like terms: 0 + 12.88888889 = 12.88888889
-7.444444444x + x2 = 12.88888889

The x term is -7.444444444x.  Take half its coefficient (-3.722222222).
Square it (13.85493827) and add it to both sides.

Add '13.85493827' to each side of the equation.
-7.444444444x + 13.85493827 + x2 = 12.88888889 + 13.85493827

Reorder the terms:
13.85493827 + -7.444444444x + x2 = 12.88888889 + 13.85493827

Combine like terms: 12.88888889 + 13.85493827 = 26.74382716
13.85493827 + -7.444444444x + x2 = 26.74382716

Factor a perfect square on the left side:
(x + -3.722222222)(x + -3.722222222) = 26.74382716

Calculate the square root of the right side: 5.171443431

Break this problem into two subproblems by setting 
(x + -3.722222222) equal to 5.171443431 and -5.171443431.

Subproblem 1

x + -3.722222222 = 5.171443431 Simplifying x + -3.722222222 = 5.171443431 Reorder the terms: -3.722222222 + x = 5.171443431 Solving -3.722222222 + x = 5.171443431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.722222222' to each side of the equation. -3.722222222 + 3.722222222 + x = 5.171443431 + 3.722222222 Combine like terms: -3.722222222 + 3.722222222 = 0.000000000 0.000000000 + x = 5.171443431 + 3.722222222 x = 5.171443431 + 3.722222222 Combine like terms: 5.171443431 + 3.722222222 = 8.893665653 x = 8.893665653 Simplifying x = 8.893665653

Subproblem 2

x + -3.722222222 = -5.171443431 Simplifying x + -3.722222222 = -5.171443431 Reorder the terms: -3.722222222 + x = -5.171443431 Solving -3.722222222 + x = -5.171443431 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.722222222' to each side of the equation. -3.722222222 + 3.722222222 + x = -5.171443431 + 3.722222222 Combine like terms: -3.722222222 + 3.722222222 = 0.000000000 0.000000000 + x = -5.171443431 + 3.722222222 x = -5.171443431 + 3.722222222 Combine like terms: -5.171443431 + 3.722222222 = -1.449221209 x = -1.449221209 Simplifying x = -1.449221209

Solution

The solution to the problem is based on the solutions from the subproblems. x = {8.893665653, -1.449221209}

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