-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 = 3.1875
5.0625 + -4.5x + x2 = 3.1875

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 3.1875

Calculate the square root of the right side: 1.785357107

Break this problem into two subproblems by setting 
(x + -2.25) equal to 1.785357107 and -1.785357107.


Subproblem 1
x + -2.25 = 1.785357107

Simplifying
x + -2.25 = 1.785357107

Reorder the terms:
-2.25 + x = 1.785357107

Solving
-2.25 + x = 1.785357107

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 = 1.785357107 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 1.785357107 + 2.25
x = 1.785357107 + 2.25

Combine like terms: 1.785357107 + 2.25 = 4.035357107
x = 4.035357107

Simplifying
x = 4.035357107


Subproblem 2
x + -2.25 = -1.785357107

Simplifying
x + -2.25 = -1.785357107

Reorder the terms:
-2.25 + x = -1.785357107

Solving
-2.25 + x = -1.785357107

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 = -1.785357107 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -1.785357107 + 2.25
x = -1.785357107 + 2.25

Combine like terms: -1.785357107 + 2.25 = 0.464642893
x = 0.464642893

Simplifying
x = 0.464642893


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.035357107, 0.464642893}
Solution
x = {4.035357107, 0.464642893}

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