6x^2-24x-17=0

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Solution for 6x^2-24x-17=0 equation: 


Simplifying
6x2 + -24x + -17 = 0

Reorder the terms:
-17 + -24x + 6x2 = 0

Solving
-17 + -24x + 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'.
-2.833333333 + -4x + x2 = 0

Move the constant term to the right:

Add '2.833333333' to each side of the equation.
-2.833333333 + -4x + 2.833333333 + x2 = 0 + 2.833333333

Reorder the terms:
-2.833333333 + 2.833333333 + -4x + x2 = 0 + 2.833333333

Combine like terms: -2.833333333 + 2.833333333 = 0.000000000
0.000000000 + -4x + x2 = 0 + 2.833333333
-4x + x2 = 0 + 2.833333333

Combine like terms: 0 + 2.833333333 = 2.833333333
-4x + x2 = 2.833333333

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 2.833333333 + 4

Reorder the terms:
4 + -4x + x2 = 2.833333333 + 4

Combine like terms: 2.833333333 + 4 = 6.833333333
4 + -4x + x2 = 6.833333333

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6.833333333

Calculate the square root of the right side: 2.614064523

Break this problem into two subproblems by setting 
(x + -2) equal to 2.614064523 and -2.614064523.


Subproblem 1
x + -2 = 2.614064523

Simplifying
x + -2 = 2.614064523

Reorder the terms:
-2 + x = 2.614064523

Solving
-2 + x = 2.614064523

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.614064523 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.614064523 + 2
x = 2.614064523 + 2

Combine like terms: 2.614064523 + 2 = 4.614064523
x = 4.614064523

Simplifying
x = 4.614064523


Subproblem 2
x + -2 = -2.614064523

Simplifying
x + -2 = -2.614064523

Reorder the terms:
-2 + x = -2.614064523

Solving
-2 + x = -2.614064523

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.614064523 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.614064523 + 2
x = -2.614064523 + 2

Combine like terms: -2.614064523 + 2 = -0.614064523
x = -0.614064523

Simplifying
x = -0.614064523


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.614064523, -0.614064523}

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