4x^2+49x+16=0

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Solution for 4x^2+49x+16=0 equation: 


Simplifying
4x2 + 49x + 16 = 0

Reorder the terms:
16 + 49x + 4x2 = 0

Solving
16 + 49x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
4 + 12.25x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 12.25x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 12.25x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 12.25x + x2 = 0 + -4
12.25x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
12.25x + x2 = -4

The x term is 12.25x.  Take half its coefficient (6.125).
Square it (37.515625) and add it to both sides.

Add '37.515625' to each side of the equation.
12.25x + 37.515625 + x2 = -4 + 37.515625

Reorder the terms:
37.515625 + 12.25x + x2 = -4 + 37.515625

Combine like terms: -4 + 37.515625 = 33.515625
37.515625 + 12.25x + x2 = 33.515625

Factor a perfect square on the left side:
(x + 6.125)(x + 6.125) = 33.515625

Calculate the square root of the right side: 5.789268088

Break this problem into two subproblems by setting 
(x + 6.125) equal to 5.789268088 and -5.789268088.


Subproblem 1
x + 6.125 = 5.789268088

Simplifying
x + 6.125 = 5.789268088

Reorder the terms:
6.125 + x = 5.789268088

Solving
6.125 + x = 5.789268088

Solving for variable 'x'.

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

Add '-6.125' to each side of the equation.
6.125 + -6.125 + x = 5.789268088 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + x = 5.789268088 + -6.125
x = 5.789268088 + -6.125

Combine like terms: 5.789268088 + -6.125 = -0.335731912
x = -0.335731912

Simplifying
x = -0.335731912


Subproblem 2
x + 6.125 = -5.789268088

Simplifying
x + 6.125 = -5.789268088

Reorder the terms:
6.125 + x = -5.789268088

Solving
6.125 + x = -5.789268088

Solving for variable 'x'.

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

Add '-6.125' to each side of the equation.
6.125 + -6.125 + x = -5.789268088 + -6.125

Combine like terms: 6.125 + -6.125 = 0.000
0.000 + x = -5.789268088 + -6.125
x = -5.789268088 + -6.125

Combine like terms: -5.789268088 + -6.125 = -11.914268088
x = -11.914268088

Simplifying
x = -11.914268088


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.335731912, -11.914268088}

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