-16x^2+72x+4=20

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Solution for -16x^2+72x+4=20 equation: 


Simplifying
-16x2 + 72x + 4 = 20

Reorder the terms:
4 + 72x + -16x2 = 20

Solving
4 + 72x + -16x2 = 20

Solving for variable 'x'.

Reorder the terms:
4 + -20 + 72x + -16x2 = 20 + -20

Combine like terms: 4 + -20 = -16
-16 + 72x + -16x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-16 + 72x + -16x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-2 + 9x + -2x2) = 0

Ignore the factor 8.

Subproblem 1
Set the factor '(-2 + 9x + -2x2)' equal to zero and attempt to solve:

Simplifying
-2 + 9x + -2x2 = 0

Solving
-2 + 9x + -2x2 = 0

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

Divide each side by '-2'.
1 + -4.5x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + -4.5x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + -4.5x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4.5x + x2 = 0 + -1
-4.5x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
-4.5x + x2 = -1

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 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = -1 + 5.0625

Combine like terms: -1 + 5.0625 = 4.0625
5.0625 + -4.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + -2.25) equal to 2.015564437 and -2.015564437.


Subproblem 1
x + -2.25 = 2.015564437

Simplifying
x + -2.25 = 2.015564437

Reorder the terms:
-2.25 + x = 2.015564437

Solving
-2.25 + x = 2.015564437

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 = 2.015564437 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 2.015564437 + 2.25
x = 2.015564437 + 2.25

Combine like terms: 2.015564437 + 2.25 = 4.265564437
x = 4.265564437

Simplifying
x = 4.265564437


Subproblem 2
x + -2.25 = -2.015564437

Simplifying
x + -2.25 = -2.015564437

Reorder the terms:
-2.25 + x = -2.015564437

Solving
-2.25 + x = -2.015564437

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 = -2.015564437 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -2.015564437 + 2.25
x = -2.015564437 + 2.25

Combine like terms: -2.015564437 + 2.25 = 0.234435563
x = 0.234435563

Simplifying
x = 0.234435563


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.265564437, 0.234435563}
Solution
x = {4.265564437, 0.234435563}

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