-16x^2+72x-5=0

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Solution for -16x^2+72x-5=0 equation: 


Simplifying
-16x2 + 72x + -5 = 0

Reorder the terms:
-5 + 72x + -16x2 = 0

Solving
-5 + 72x + -16x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-16 the coefficient of the squared term: 

Divide each side by '-16'.
0.3125 + -4.5x + x2 = 0

Move the constant term to the right:

Add '-0.3125' to each side of the equation.
0.3125 + -4.5x + -0.3125 + x2 = 0 + -0.3125

Reorder the terms:
0.3125 + -0.3125 + -4.5x + x2 = 0 + -0.3125

Combine like terms: 0.3125 + -0.3125 = 0.0000
0.0000 + -4.5x + x2 = 0 + -0.3125
-4.5x + x2 = 0 + -0.3125

Combine like terms: 0 + -0.3125 = -0.3125
-4.5x + x2 = -0.3125

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 = -0.3125 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -0.3125 + 5.0625

Combine like terms: -0.3125 + 5.0625 = 4.75
5.0625 + -4.5x + x2 = 4.75

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 4.75

Calculate the square root of the right side: 2.179449472

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.179449472 and -2.179449472.


Subproblem 1
x + -2.25 = 2.179449472

Simplifying
x + -2.25 = 2.179449472

Reorder the terms:
-2.25 + x = 2.179449472

Solving
-2.25 + x = 2.179449472

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 = 2.179449472 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.179449472 + 2.25
x = 2.179449472 + 2.25

Combine like terms: 2.179449472 + 2.25 = 4.429449472
x = 4.429449472

Simplifying
x = 4.429449472


Subproblem 2
x + -2.25 = -2.179449472

Simplifying
x + -2.25 = -2.179449472

Reorder the terms:
-2.25 + x = -2.179449472

Solving
-2.25 + x = -2.179449472

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 = -2.179449472 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.179449472 + 2.25
x = -2.179449472 + 2.25

Combine like terms: -2.179449472 + 2.25 = 0.070550528
x = 0.070550528

Simplifying
x = 0.070550528


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.429449472, 0.070550528}

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