24x^2-2x-3=0

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Solution for 24x^2-2x-3=0 equation: 


Simplifying
24x2 + -2x + -3 = 0

Reorder the terms:
-3 + -2x + 24x2 = 0

Solving
-3 + -2x + 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'.
-0.125 + -0.08333333333x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + -0.08333333333x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + -0.08333333333x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + -0.08333333333x + x2 = 0 + 0.125
-0.08333333333x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
-0.08333333333x + x2 = 0.125

The x term is -0.08333333333x.  Take half its coefficient (-0.04166666667).
Square it (0.001736111111) and add it to both sides.

Add '0.001736111111' to each side of the equation.
-0.08333333333x + 0.001736111111 + x2 = 0.125 + 0.001736111111

Reorder the terms:
0.001736111111 + -0.08333333333x + x2 = 0.125 + 0.001736111111

Combine like terms: 0.125 + 0.001736111111 = 0.126736111111
0.001736111111 + -0.08333333333x + x2 = 0.126736111111

Factor a perfect square on the left side:
(x + -0.04166666667)(x + -0.04166666667) = 0.126736111111

Calculate the square root of the right side: 0.356000156

Break this problem into two subproblems by setting 
(x + -0.04166666667) equal to 0.356000156 and -0.356000156.


Subproblem 1
x + -0.04166666667 = 0.356000156

Simplifying
x + -0.04166666667 = 0.356000156

Reorder the terms:
-0.04166666667 + x = 0.356000156

Solving
-0.04166666667 + x = 0.356000156

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = 0.356000156 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = 0.356000156 + 0.04166666667
x = 0.356000156 + 0.04166666667

Combine like terms: 0.356000156 + 0.04166666667 = 0.39766682267
x = 0.39766682267

Simplifying
x = 0.39766682267


Subproblem 2
x + -0.04166666667 = -0.356000156

Simplifying
x + -0.04166666667 = -0.356000156

Reorder the terms:
-0.04166666667 + x = -0.356000156

Solving
-0.04166666667 + x = -0.356000156

Solving for variable 'x'.

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

Add '0.04166666667' to each side of the equation.
-0.04166666667 + 0.04166666667 + x = -0.356000156 + 0.04166666667

Combine like terms: -0.04166666667 + 0.04166666667 = 0.00000000000
0.00000000000 + x = -0.356000156 + 0.04166666667
x = -0.356000156 + 0.04166666667

Combine like terms: -0.356000156 + 0.04166666667 = -0.31433348933
x = -0.31433348933

Simplifying
x = -0.31433348933


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.39766682267, -0.31433348933}

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