-16x^2+72x+84=0

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Solution for -16x^2+72x+84=0 equation: 


Simplifying
-16x2 + 72x + 84 = 0

Reorder the terms:
84 + 72x + -16x2 = 0

Solving
84 + 72x + -16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(21 + 18x + -4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(21 + 18x + -4x2)' equal to zero and attempt to solve:

Simplifying
21 + 18x + -4x2 = 0

Solving
21 + 18x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-5.25 + -4.5x + x2 = 0

Move the constant term to the right:

Add '5.25' to each side of the equation.
-5.25 + -4.5x + 5.25 + x2 = 0 + 5.25

Reorder the terms:
-5.25 + 5.25 + -4.5x + x2 = 0 + 5.25

Combine like terms: -5.25 + 5.25 = 0.00
0.00 + -4.5x + x2 = 0 + 5.25
-4.5x + x2 = 0 + 5.25

Combine like terms: 0 + 5.25 = 5.25
-4.5x + x2 = 5.25

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 = 5.25 + 5.0625

Reorder the terms:
5.0625 + -4.5x + x2 = 5.25 + 5.0625

Combine like terms: 5.25 + 5.0625 = 10.3125
5.0625 + -4.5x + x2 = 10.3125

Factor a perfect square on the left side:
(x + -2.25)(x + -2.25) = 10.3125

Calculate the square root of the right side: 3.211308145

Break this problem into two subproblems by setting 
(x + -2.25) equal to 3.211308145 and -3.211308145.


Subproblem 1
x + -2.25 = 3.211308145

Simplifying
x + -2.25 = 3.211308145

Reorder the terms:
-2.25 + x = 3.211308145

Solving
-2.25 + x = 3.211308145

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 = 3.211308145 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = 3.211308145 + 2.25
x = 3.211308145 + 2.25

Combine like terms: 3.211308145 + 2.25 = 5.461308145
x = 5.461308145

Simplifying
x = 5.461308145


Subproblem 2
x + -2.25 = -3.211308145

Simplifying
x + -2.25 = -3.211308145

Reorder the terms:
-2.25 + x = -3.211308145

Solving
-2.25 + x = -3.211308145

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 = -3.211308145 + 2.25

Combine like terms: -2.25 + 2.25 = 0.00
0.00 + x = -3.211308145 + 2.25
x = -3.211308145 + 2.25

Combine like terms: -3.211308145 + 2.25 = -0.961308145
x = -0.961308145

Simplifying
x = -0.961308145


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.461308145, -0.961308145}
Solution
x = {5.461308145, -0.961308145}

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