16x^2+24x-576=0

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Solution for 16x^2+24x-576=0 equation: 


Simplifying
16x2 + 24x + -576 = 0

Reorder the terms:
-576 + 24x + 16x2 = 0

Solving
-576 + 24x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-72 + 3x + 2x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-72 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-72 + 3x + 2x2 = 0

Solving
-72 + 3x + 2x2 = 0

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

Divide each side by '2'.
-36 + 1.5x + x2 = 0

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 1.5x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 1.5x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 1.5x + x2 = 0 + 36
1.5x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
1.5x + x2 = 36

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 36 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 36 + 0.5625

Combine like terms: 36 + 0.5625 = 36.5625
0.5625 + 1.5x + x2 = 36.5625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 36.5625

Calculate the square root of the right side: 6.046693311

Break this problem into two subproblems by setting 
(x + 0.75) equal to 6.046693311 and -6.046693311.


Subproblem 1
x + 0.75 = 6.046693311

Simplifying
x + 0.75 = 6.046693311

Reorder the terms:
0.75 + x = 6.046693311

Solving
0.75 + x = 6.046693311

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 6.046693311 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 6.046693311 + -0.75
x = 6.046693311 + -0.75

Combine like terms: 6.046693311 + -0.75 = 5.296693311
x = 5.296693311

Simplifying
x = 5.296693311


Subproblem 2
x + 0.75 = -6.046693311

Simplifying
x + 0.75 = -6.046693311

Reorder the terms:
0.75 + x = -6.046693311

Solving
0.75 + x = -6.046693311

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -6.046693311 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -6.046693311 + -0.75
x = -6.046693311 + -0.75

Combine like terms: -6.046693311 + -0.75 = -6.796693311
x = -6.796693311

Simplifying
x = -6.796693311


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.296693311, -6.796693311}
Solution
x = {5.296693311, -6.796693311}

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