-16x^2+72x+30=0

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Solution for -16x^2+72x+30=0 equation: 


Simplifying
-16x2 + 72x + 30 = 0

Reorder the terms:
30 + 72x + -16x2 = 0

Solving
30 + 72x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(15 + 36x + -8x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(15 + 36x + -8x2)' equal to zero and attempt to solve:

Simplifying
15 + 36x + -8x2 = 0

Solving
15 + 36x + -8x2 = 0

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

Divide each side by '-8'.
-1.875 + -4.5x + x2 = 0

Move the constant term to the right:

Add '1.875' to each side of the equation.
-1.875 + -4.5x + 1.875 + x2 = 0 + 1.875

Reorder the terms:
-1.875 + 1.875 + -4.5x + x2 = 0 + 1.875

Combine like terms: -1.875 + 1.875 = 0.000
0.000 + -4.5x + x2 = 0 + 1.875
-4.5x + x2 = 0 + 1.875

Combine like terms: 0 + 1.875 = 1.875
-4.5x + x2 = 1.875

The x term is -4.5x.  Take half its coefficient (-2.25).
Square it (5.0625) and add it to both sides.

Add '5.0625' to each side of the equation.
-4.5x + 5.0625 + x2 = 1.875 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 1.875 + 5.0625

Combine like terms: 1.875 + 5.0625 = 6.9375
5.0625 + -4.5x + x2 = 6.9375

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 6.9375

Calculate the square root of the right side: 2.633913438

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.633913438 and -2.633913438.


Subproblem 1
x + -2.25 = 2.633913438

Simplifying
x + -2.25 = 2.633913438

Reorder the terms:
-2.25 + x = 2.633913438

Solving
-2.25 + x = 2.633913438

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = 2.633913438 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.633913438 + 2.25
x = 2.633913438 + 2.25

Combine like terms: 2.633913438 + 2.25 = 4.883913438
x = 4.883913438

Simplifying
x = 4.883913438


Subproblem 2
x + -2.25 = -2.633913438

Simplifying
x + -2.25 = -2.633913438

Reorder the terms:
-2.25 + x = -2.633913438

Solving
-2.25 + x = -2.633913438

Solving for variable 'x'.

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

Add '2.25' to each side of the equation.
-2.25 + 2.25 + x = -2.633913438 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.633913438 + 2.25
x = -2.633913438 + 2.25

Combine like terms: -2.633913438 + 2.25 = -0.383913438
x = -0.383913438

Simplifying
x = -0.383913438


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.883913438, -0.383913438}
Solution
x = {4.883913438, -0.383913438}

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