3x^2-6x-34=0

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Solution for 3x^2-6x-34=0 equation:


Simplifying
3x2 + -6x + -34 = 0

Reorder the terms:
-34 + -6x + 3x2 = 0

Solving
-34 + -6x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
-11.33333333 + -2x + x2 = 0

Move the constant term to the right:

Add '11.33333333' to each side of the equation.
-11.33333333 + -2x + 11.33333333 + x2 = 0 + 11.33333333

Reorder the terms:
-11.33333333 + 11.33333333 + -2x + x2 = 0 + 11.33333333

Combine like terms: -11.33333333 + 11.33333333 = 0.00000000
0.00000000 + -2x + x2 = 0 + 11.33333333
-2x + x2 = 0 + 11.33333333

Combine like terms: 0 + 11.33333333 = 11.33333333
-2x + x2 = 11.33333333

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 11.33333333 + 1

Reorder the terms:
1 + -2x + x2 = 11.33333333 + 1

Combine like terms: 11.33333333 + 1 = 12.33333333
1 + -2x + x2 = 12.33333333

Factor a perfect square on the left side:
(x + -1)(x + -1) = 12.33333333

Calculate the square root of the right side: 3.511884584

Break this problem into two subproblems by setting 
(x + -1) equal to 3.511884584 and -3.511884584.

Subproblem 1

x + -1 = 3.511884584 Simplifying x + -1 = 3.511884584 Reorder the terms: -1 + x = 3.511884584 Solving -1 + x = 3.511884584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 3.511884584 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.511884584 + 1 x = 3.511884584 + 1 Combine like terms: 3.511884584 + 1 = 4.511884584 x = 4.511884584 Simplifying x = 4.511884584

Subproblem 2

x + -1 = -3.511884584 Simplifying x + -1 = -3.511884584 Reorder the terms: -1 + x = -3.511884584 Solving -1 + x = -3.511884584 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -3.511884584 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.511884584 + 1 x = -3.511884584 + 1 Combine like terms: -3.511884584 + 1 = -2.511884584 x = -2.511884584 Simplifying x = -2.511884584

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.511884584, -2.511884584}

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