24x^2-3x-18=0

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Solution for 24x^2-3x-18=0 equation: 


Simplifying
24x2 + -3x + -18 = 0

Reorder the terms:
-18 + -3x + 24x2 = 0

Solving
-18 + -3x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-6 + -1x + 8x2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(-6 + -1x + 8x2)' equal to zero and attempt to solve:

Simplifying
-6 + -1x + 8x2 = 0

Solving
-6 + -1x + 8x2 = 0

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

Divide each side by '8'.
-0.75 + -0.125x + x2 = 0

Move the constant term to the right:

Add '0.75' to each side of the equation.
-0.75 + -0.125x + 0.75 + x2 = 0 + 0.75

Reorder the terms:
-0.75 + 0.75 + -0.125x + x2 = 0 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + -0.125x + x2 = 0 + 0.75
-0.125x + x2 = 0 + 0.75

Combine like terms: 0 + 0.75 = 0.75
-0.125x + x2 = 0.75

The x term is -0.125x.  Take half its coefficient (-0.0625).
Square it (0.00390625) and add it to both sides.

Add '0.00390625' to each side of the equation.
-0.125x + 0.00390625 + x2 = 0.75 + 0.00390625

Reorder the terms:
0.00390625 + -0.125x + x2 = 0.75 + 0.00390625

Combine like terms: 0.75 + 0.00390625 = 0.75390625
0.00390625 + -0.125x + x2 = 0.75390625

Factor a perfect square on the left side:
(x + -0.0625)(x + -0.0625) = 0.75390625

Calculate the square root of the right side: 0.868277749

Break this problem into two subproblems by setting 
(x + -0.0625) equal to 0.868277749 and -0.868277749.


Subproblem 1
x + -0.0625 = 0.868277749

Simplifying
x + -0.0625 = 0.868277749

Reorder the terms:
-0.0625 + x = 0.868277749

Solving
-0.0625 + x = 0.868277749

Solving for variable 'x'.

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

Add '0.0625' to each side of the equation.
-0.0625 + 0.0625 + x = 0.868277749 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + x = 0.868277749 + 0.0625
x = 0.868277749 + 0.0625

Combine like terms: 0.868277749 + 0.0625 = 0.930777749
x = 0.930777749

Simplifying
x = 0.930777749


Subproblem 2
x + -0.0625 = -0.868277749

Simplifying
x + -0.0625 = -0.868277749

Reorder the terms:
-0.0625 + x = -0.868277749

Solving
-0.0625 + x = -0.868277749

Solving for variable 'x'.

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

Add '0.0625' to each side of the equation.
-0.0625 + 0.0625 + x = -0.868277749 + 0.0625

Combine like terms: -0.0625 + 0.0625 = 0.0000
0.0000 + x = -0.868277749 + 0.0625
x = -0.868277749 + 0.0625

Combine like terms: -0.868277749 + 0.0625 = -0.805777749
x = -0.805777749

Simplifying
x = -0.805777749


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.930777749, -0.805777749}
Solution
x = {0.930777749, -0.805777749}

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