24x^2-17x-6=0

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


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

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

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

Solving for variable 'x'.

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

Divide each side by '24'.
-0.25 + -0.7083333333x + x2 = 0

Move the constant term to the right:

Add '0.25' to each side of the equation.
-0.25 + -0.7083333333x + 0.25 + x2 = 0 + 0.25

Reorder the terms:
-0.25 + 0.25 + -0.7083333333x + x2 = 0 + 0.25

Combine like terms: -0.25 + 0.25 = 0.00
0.00 + -0.7083333333x + x2 = 0 + 0.25
-0.7083333333x + x2 = 0 + 0.25

Combine like terms: 0 + 0.25 = 0.25
-0.7083333333x + x2 = 0.25

The x term is -0.7083333333x.  Take half its coefficient (-0.3541666667).
Square it (0.1254340278) and add it to both sides.

Add '0.1254340278' to each side of the equation.
-0.7083333333x + 0.1254340278 + x2 = 0.25 + 0.1254340278

Reorder the terms:
0.1254340278 + -0.7083333333x + x2 = 0.25 + 0.1254340278

Combine like terms: 0.25 + 0.1254340278 = 0.3754340278
0.1254340278 + -0.7083333333x + x2 = 0.3754340278

Factor a perfect square on the left side:
(x + -0.3541666667)(x + -0.3541666667) = 0.3754340278

Calculate the square root of the right side: 0.612726715

Break this problem into two subproblems by setting 
(x + -0.3541666667) equal to 0.612726715 and -0.612726715.


Subproblem 1
x + -0.3541666667 = 0.612726715

Simplifying
x + -0.3541666667 = 0.612726715

Reorder the terms:
-0.3541666667 + x = 0.612726715

Solving
-0.3541666667 + x = 0.612726715

Solving for variable 'x'.

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

Add '0.3541666667' to each side of the equation.
-0.3541666667 + 0.3541666667 + x = 0.612726715 + 0.3541666667

Combine like terms: -0.3541666667 + 0.3541666667 = 0.0000000000
0.0000000000 + x = 0.612726715 + 0.3541666667
x = 0.612726715 + 0.3541666667

Combine like terms: 0.612726715 + 0.3541666667 = 0.9668933817
x = 0.9668933817

Simplifying
x = 0.9668933817


Subproblem 2
x + -0.3541666667 = -0.612726715

Simplifying
x + -0.3541666667 = -0.612726715

Reorder the terms:
-0.3541666667 + x = -0.612726715

Solving
-0.3541666667 + x = -0.612726715

Solving for variable 'x'.

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

Add '0.3541666667' to each side of the equation.
-0.3541666667 + 0.3541666667 + x = -0.612726715 + 0.3541666667

Combine like terms: -0.3541666667 + 0.3541666667 = 0.0000000000
0.0000000000 + x = -0.612726715 + 0.3541666667
x = -0.612726715 + 0.3541666667

Combine like terms: -0.612726715 + 0.3541666667 = -0.2585600483
x = -0.2585600483

Simplifying
x = -0.2585600483


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.9668933817, -0.2585600483}

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