6x^2-18x-77=0

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Solution for 6x^2-18x-77=0 equation:


Simplifying
6x2 + -18x + -77 = 0

Reorder the terms:
-77 + -18x + 6x2 = 0

Solving
-77 + -18x + 6x2 = 0

Solving for variable 'x'.

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

Divide each side by '6'.
-12.83333333 + -3x + x2 = 0

Move the constant term to the right:

Add '12.83333333' to each side of the equation.
-12.83333333 + -3x + 12.83333333 + x2 = 0 + 12.83333333

Reorder the terms:
-12.83333333 + 12.83333333 + -3x + x2 = 0 + 12.83333333

Combine like terms: -12.83333333 + 12.83333333 = 0.00000000
0.00000000 + -3x + x2 = 0 + 12.83333333
-3x + x2 = 0 + 12.83333333

Combine like terms: 0 + 12.83333333 = 12.83333333
-3x + x2 = 12.83333333

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 12.83333333 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 12.83333333 + 2.25

Combine like terms: 12.83333333 + 2.25 = 15.08333333
2.25 + -3x + x2 = 15.08333333

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 15.08333333

Calculate the square root of the right side: 3.883726732

Break this problem into two subproblems by setting 
(x + -1.5) equal to 3.883726732 and -3.883726732.

Subproblem 1

x + -1.5 = 3.883726732 Simplifying x + -1.5 = 3.883726732 Reorder the terms: -1.5 + x = 3.883726732 Solving -1.5 + x = 3.883726732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.883726732 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.883726732 + 1.5 x = 3.883726732 + 1.5 Combine like terms: 3.883726732 + 1.5 = 5.383726732 x = 5.383726732 Simplifying x = 5.383726732

Subproblem 2

x + -1.5 = -3.883726732 Simplifying x + -1.5 = -3.883726732 Reorder the terms: -1.5 + x = -3.883726732 Solving -1.5 + x = -3.883726732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.883726732 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.883726732 + 1.5 x = -3.883726732 + 1.5 Combine like terms: -3.883726732 + 1.5 = -2.383726732 x = -2.383726732 Simplifying x = -2.383726732

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.383726732, -2.383726732}

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