16x^2+52x+4=0

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Solution for 16x^2+52x+4=0 equation: 


Simplifying
16x2 + 52x + 4 = 0

Reorder the terms:
4 + 52x + 16x2 = 0

Solving
4 + 52x + 16x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 13x + 4x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(1 + 13x + 4x2)' equal to zero and attempt to solve:

Simplifying
1 + 13x + 4x2 = 0

Solving
1 + 13x + 4x2 = 0

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

Divide each side by '4'.
0.25 + 3.25x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 3.25x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 3.25x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 3.25x + x2 = 0 + -0.25
3.25x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
3.25x + x2 = -0.25

The x term is 3.25x.  Take half its coefficient (1.625).
Square it (2.640625) and add it to both sides.

Add '2.640625' to each side of the equation.
3.25x + 2.640625 + x2 = -0.25 + 2.640625

Reorder the terms:
2.640625 + 3.25x + x2 = -0.25 + 2.640625

Combine like terms: -0.25 + 2.640625 = 2.390625
2.640625 + 3.25x + x2 = 2.390625

Factor a perfect square on the left side:
(x + 1.625)(x + 1.625) = 2.390625

Calculate the square root of the right side: 1.54616461

Break this problem into two subproblems by setting 
(x + 1.625) equal to 1.54616461 and -1.54616461.


Subproblem 1
x + 1.625 = 1.54616461

Simplifying
x + 1.625 = 1.54616461

Reorder the terms:
1.625 + x = 1.54616461

Solving
1.625 + x = 1.54616461

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = 1.54616461 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = 1.54616461 + -1.625
x = 1.54616461 + -1.625

Combine like terms: 1.54616461 + -1.625 = -0.07883539
x = -0.07883539

Simplifying
x = -0.07883539


Subproblem 2
x + 1.625 = -1.54616461

Simplifying
x + 1.625 = -1.54616461

Reorder the terms:
1.625 + x = -1.54616461

Solving
1.625 + x = -1.54616461

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '-1.625' to each side of the equation.
1.625 + -1.625 + x = -1.54616461 + -1.625

Combine like terms: 1.625 + -1.625 = 0.000
0.000 + x = -1.54616461 + -1.625
x = -1.54616461 + -1.625

Combine like terms: -1.54616461 + -1.625 = -3.17116461
x = -3.17116461

Simplifying
x = -3.17116461


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.07883539, -3.17116461}
Solution
x = {-0.07883539, -3.17116461}

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