24x^2+4x-3=0

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Solution for 24x^2+4x-3=0 equation: 


Simplifying
24x2 + 4x + -3 = 0

Reorder the terms:
-3 + 4x + 24x2 = 0

Solving
-3 + 4x + 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 + 0.1666666667x + x2 = 0

Move the constant term to the right:

Add '0.125' to each side of the equation.
-0.125 + 0.1666666667x + 0.125 + x2 = 0 + 0.125

Reorder the terms:
-0.125 + 0.125 + 0.1666666667x + x2 = 0 + 0.125

Combine like terms: -0.125 + 0.125 = 0.000
0.000 + 0.1666666667x + x2 = 0 + 0.125
0.1666666667x + x2 = 0 + 0.125

Combine like terms: 0 + 0.125 = 0.125
0.1666666667x + x2 = 0.125

The x term is 0.1666666667x.  Take half its coefficient (0.08333333335).
Square it (0.006944444447) and add it to both sides.

Add '0.006944444447' to each side of the equation.
0.1666666667x + 0.006944444447 + x2 = 0.125 + 0.006944444447

Reorder the terms:
0.006944444447 + 0.1666666667x + x2 = 0.125 + 0.006944444447

Combine like terms: 0.125 + 0.006944444447 = 0.131944444447
0.006944444447 + 0.1666666667x + x2 = 0.131944444447

Factor a perfect square on the left side:
(x + 0.08333333335)(x + 0.08333333335) = 0.131944444447

Calculate the square root of the right side: 0.363241579

Break this problem into two subproblems by setting 
(x + 0.08333333335) equal to 0.363241579 and -0.363241579.


Subproblem 1
x + 0.08333333335 = 0.363241579

Simplifying
x + 0.08333333335 = 0.363241579

Reorder the terms:
0.08333333335 + x = 0.363241579

Solving
0.08333333335 + x = 0.363241579

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = 0.363241579 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = 0.363241579 + -0.08333333335
x = 0.363241579 + -0.08333333335

Combine like terms: 0.363241579 + -0.08333333335 = 0.27990824565
x = 0.27990824565

Simplifying
x = 0.27990824565


Subproblem 2
x + 0.08333333335 = -0.363241579

Simplifying
x + 0.08333333335 = -0.363241579

Reorder the terms:
0.08333333335 + x = -0.363241579

Solving
0.08333333335 + x = -0.363241579

Solving for variable 'x'.

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

Add '-0.08333333335' to each side of the equation.
0.08333333335 + -0.08333333335 + x = -0.363241579 + -0.08333333335

Combine like terms: 0.08333333335 + -0.08333333335 = 0.00000000000
0.00000000000 + x = -0.363241579 + -0.08333333335
x = -0.363241579 + -0.08333333335

Combine like terms: -0.363241579 + -0.08333333335 = -0.44657491235
x = -0.44657491235

Simplifying
x = -0.44657491235


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.27990824565, -0.44657491235}

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