24x^2+30x+8=0

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Solution for 24x^2+30x+8=0 equation: 


Simplifying
24x2 + 30x + 8 = 0

Reorder the terms:
8 + 30x + 24x2 = 0

Solving
8 + 30x + 24x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 15x + 12x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + 15x + 12x2)' equal to zero and attempt to solve:

Simplifying
4 + 15x + 12x2 = 0

Solving
4 + 15x + 12x2 = 0

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

Divide each side by '12'.
0.3333333333 + 1.25x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + 1.25x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + 1.25x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + 1.25x + x2 = 0 + -0.3333333333
1.25x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
1.25x + x2 = -0.3333333333

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = -0.3333333333 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = -0.3333333333 + 0.390625

Combine like terms: -0.3333333333 + 0.390625 = 0.0572916667
0.390625 + 1.25x + x2 = 0.0572916667

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 0.0572916667

Calculate the square root of the right side: 0.239356777

Break this problem into two subproblems by setting 
(x + 0.625) equal to 0.239356777 and -0.239356777.


Subproblem 1
x + 0.625 = 0.239356777

Simplifying
x + 0.625 = 0.239356777

Reorder the terms:
0.625 + x = 0.239356777

Solving
0.625 + x = 0.239356777

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = 0.239356777 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = 0.239356777 + -0.625
x = 0.239356777 + -0.625

Combine like terms: 0.239356777 + -0.625 = -0.385643223
x = -0.385643223

Simplifying
x = -0.385643223


Subproblem 2
x + 0.625 = -0.239356777

Simplifying
x + 0.625 = -0.239356777

Reorder the terms:
0.625 + x = -0.239356777

Solving
0.625 + x = -0.239356777

Solving for variable 'x'.

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

Add '-0.625' to each side of the equation.
0.625 + -0.625 + x = -0.239356777 + -0.625

Combine like terms: 0.625 + -0.625 = 0.000
0.000 + x = -0.239356777 + -0.625
x = -0.239356777 + -0.625

Combine like terms: -0.239356777 + -0.625 = -0.864356777
x = -0.864356777

Simplifying
x = -0.864356777


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.385643223, -0.864356777}
Solution
x = {-0.385643223, -0.864356777}

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