-4x^2+-16x-3=0

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Solution for -4x^2+-16x-3=0 equation: 


Simplifying
-4x2 + -16x + -3 = 0

Reorder the terms:
-3 + -16x + -4x2 = 0

Solving
-3 + -16x + -4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(3 + 16x + 4x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(3 + 16x + 4x2)' equal to zero and attempt to solve:

Simplifying
3 + 16x + 4x2 = 0

Solving
3 + 16x + 4x2 = 0

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

Divide each side by '4'.
0.75 + 4x + x2 = 0

Move the constant term to the right:

Add '-0.75' to each side of the equation.
0.75 + 4x + -0.75 + x2 = 0 + -0.75

Reorder the terms:
0.75 + -0.75 + 4x + x2 = 0 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + 4x + x2 = 0 + -0.75
4x + x2 = 0 + -0.75

Combine like terms: 0 + -0.75 = -0.75
4x + x2 = -0.75

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -0.75 + 4

Reorder the terms:
4 + 4x + x2 = -0.75 + 4

Combine like terms: -0.75 + 4 = 3.25
4 + 4x + x2 = 3.25

Factor a perfect square on the left side:
(x + 2)(x + 2) = 3.25

Calculate the square root of the right side: 1.802775638

Break this problem into two subproblems by setting 
(x + 2) equal to 1.802775638 and -1.802775638.


Subproblem 1
x + 2 = 1.802775638

Simplifying
x + 2 = 1.802775638

Reorder the terms:
2 + x = 1.802775638

Solving
2 + x = 1.802775638

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 1.802775638 + -2

Combine like terms: 2 + -2 = 0
0 + x = 1.802775638 + -2
x = 1.802775638 + -2

Combine like terms: 1.802775638 + -2 = -0.197224362
x = -0.197224362

Simplifying
x = -0.197224362


Subproblem 2
x + 2 = -1.802775638

Simplifying
x + 2 = -1.802775638

Reorder the terms:
2 + x = -1.802775638

Solving
2 + x = -1.802775638

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -1.802775638 + -2

Combine like terms: 2 + -2 = 0
0 + x = -1.802775638 + -2
x = -1.802775638 + -2

Combine like terms: -1.802775638 + -2 = -3.802775638
x = -3.802775638

Simplifying
x = -3.802775638


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.197224362, -3.802775638}
Solution
x = {-0.197224362, -3.802775638}

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