24x^2-11x-8=

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Solution for 24x^2-11x-8= equation: 


Simplifying
24x2 + -11x + -8 = 0

Reorder the terms:
-8 + -11x + 24x2 = 0

Solving
-8 + -11x + 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'.
-0.3333333333 + -0.4583333333x + x2 = 0

Move the constant term to the right:

Add '0.3333333333' to each side of the equation.
-0.3333333333 + -0.4583333333x + 0.3333333333 + x2 = 0 + 0.3333333333

Reorder the terms:
-0.3333333333 + 0.3333333333 + -0.4583333333x + x2 = 0 + 0.3333333333

Combine like terms: -0.3333333333 + 0.3333333333 = 0.0000000000
0.0000000000 + -0.4583333333x + x2 = 0 + 0.3333333333
-0.4583333333x + x2 = 0 + 0.3333333333

Combine like terms: 0 + 0.3333333333 = 0.3333333333
-0.4583333333x + x2 = 0.3333333333

The x term is -0.4583333333x.  Take half its coefficient (-0.2291666667).
Square it (0.05251736113) and add it to both sides.

Add '0.05251736113' to each side of the equation.
-0.4583333333x + 0.05251736113 + x2 = 0.3333333333 + 0.05251736113

Reorder the terms:
0.05251736113 + -0.4583333333x + x2 = 0.3333333333 + 0.05251736113

Combine like terms: 0.3333333333 + 0.05251736113 = 0.38585069443
0.05251736113 + -0.4583333333x + x2 = 0.38585069443

Factor a perfect square on the left side:
(x + -0.2291666667)(x + -0.2291666667) = 0.38585069443

Calculate the square root of the right side: 0.621168813

Break this problem into two subproblems by setting 
(x + -0.2291666667) equal to 0.621168813 and -0.621168813.


Subproblem 1
x + -0.2291666667 = 0.621168813

Simplifying
x + -0.2291666667 = 0.621168813

Reorder the terms:
-0.2291666667 + x = 0.621168813

Solving
-0.2291666667 + x = 0.621168813

Solving for variable 'x'.

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

Add '0.2291666667' to each side of the equation.
-0.2291666667 + 0.2291666667 + x = 0.621168813 + 0.2291666667

Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000
0.0000000000 + x = 0.621168813 + 0.2291666667
x = 0.621168813 + 0.2291666667

Combine like terms: 0.621168813 + 0.2291666667 = 0.8503354797
x = 0.8503354797

Simplifying
x = 0.8503354797


Subproblem 2
x + -0.2291666667 = -0.621168813

Simplifying
x + -0.2291666667 = -0.621168813

Reorder the terms:
-0.2291666667 + x = -0.621168813

Solving
-0.2291666667 + x = -0.621168813

Solving for variable 'x'.

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

Add '0.2291666667' to each side of the equation.
-0.2291666667 + 0.2291666667 + x = -0.621168813 + 0.2291666667

Combine like terms: -0.2291666667 + 0.2291666667 = 0.0000000000
0.0000000000 + x = -0.621168813 + 0.2291666667
x = -0.621168813 + 0.2291666667

Combine like terms: -0.621168813 + 0.2291666667 = -0.3920021463
x = -0.3920021463

Simplifying
x = -0.3920021463


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.8503354797, -0.3920021463}

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