16x^2+72x+76=0

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Solution for 16x^2+72x+76=0 equation: 


Simplifying
16x2 + 72x + 76 = 0

Reorder the terms:
76 + 72x + 16x2 = 0

Solving
76 + 72x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(19 + 18x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(19 + 18x + 4x2)' equal to zero and attempt to solve:

Simplifying
19 + 18x + 4x2 = 0

Solving
19 + 18x + 4x2 = 0

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

Divide each side by '4'.
4.75 + 4.5x + x2 = 0

Move the constant term to the right:

Add '-4.75' to each side of the equation.
4.75 + 4.5x + -4.75 + x2 = 0 + -4.75

Reorder the terms:
4.75 + -4.75 + 4.5x + x2 = 0 + -4.75

Combine like terms: 4.75 + -4.75 = 0.00
0.00 + 4.5x + x2 = 0 + -4.75
4.5x + x2 = 0 + -4.75

Combine like terms: 0 + -4.75 = -4.75
4.5x + x2 = -4.75

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 = -4.75 + 5.0625

Reorder the terms:
5.0625 + 4.5x + x2 = -4.75 + 5.0625

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

Factor a perfect square on the left side:
(x + 2.25)(x + 2.25) = 0.3125

Calculate the square root of the right side: 0.559016994

Break this problem into two subproblems by setting 
(x + 2.25) equal to 0.559016994 and -0.559016994.


Subproblem 1
x + 2.25 = 0.559016994

Simplifying
x + 2.25 = 0.559016994

Reorder the terms:
2.25 + x = 0.559016994

Solving
2.25 + x = 0.559016994

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 = 0.559016994 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = 0.559016994 + -2.25
x = 0.559016994 + -2.25

Combine like terms: 0.559016994 + -2.25 = -1.690983006
x = -1.690983006

Simplifying
x = -1.690983006


Subproblem 2
x + 2.25 = -0.559016994

Simplifying
x + 2.25 = -0.559016994

Reorder the terms:
2.25 + x = -0.559016994

Solving
2.25 + x = -0.559016994

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 = -0.559016994 + -2.25

Combine like terms: 2.25 + -2.25 = 0.00
0.00 + x = -0.559016994 + -2.25
x = -0.559016994 + -2.25

Combine like terms: -0.559016994 + -2.25 = -2.809016994
x = -2.809016994

Simplifying
x = -2.809016994


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.690983006, -2.809016994}
Solution
x = {-1.690983006, -2.809016994}

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