4x^2+79x+16=0

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Solution for 4x^2+79x+16=0 equation: 


Simplifying
4x2 + 79x + 16 = 0

Reorder the terms:
16 + 79x + 4x2 = 0

Solving
16 + 79x + 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 + 19.75x + x2 = 0

Move the constant term to the right:

Add '-4' to each side of the equation.
4 + 19.75x + -4 + x2 = 0 + -4

Reorder the terms:
4 + -4 + 19.75x + x2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 19.75x + x2 = 0 + -4
19.75x + x2 = 0 + -4

Combine like terms: 0 + -4 = -4
19.75x + x2 = -4

The x term is 19.75x.  Take half its coefficient (9.875).
Square it (97.515625) and add it to both sides.

Add '97.515625' to each side of the equation.
19.75x + 97.515625 + x2 = -4 + 97.515625

Reorder the terms:
97.515625 + 19.75x + x2 = -4 + 97.515625

Combine like terms: -4 + 97.515625 = 93.515625
97.515625 + 19.75x + x2 = 93.515625

Factor a perfect square on the left side:
(x + 9.875)(x + 9.875) = 93.515625

Calculate the square root of the right side: 9.670347719

Break this problem into two subproblems by setting 
(x + 9.875) equal to 9.670347719 and -9.670347719.


Subproblem 1
x + 9.875 = 9.670347719

Simplifying
x + 9.875 = 9.670347719

Reorder the terms:
9.875 + x = 9.670347719

Solving
9.875 + x = 9.670347719

Solving for variable 'x'.

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

Add '-9.875' to each side of the equation.
9.875 + -9.875 + x = 9.670347719 + -9.875

Combine like terms: 9.875 + -9.875 = 0.000
0.000 + x = 9.670347719 + -9.875
x = 9.670347719 + -9.875

Combine like terms: 9.670347719 + -9.875 = -0.204652281
x = -0.204652281

Simplifying
x = -0.204652281


Subproblem 2
x + 9.875 = -9.670347719

Simplifying
x + 9.875 = -9.670347719

Reorder the terms:
9.875 + x = -9.670347719

Solving
9.875 + x = -9.670347719

Solving for variable 'x'.

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

Add '-9.875' to each side of the equation.
9.875 + -9.875 + x = -9.670347719 + -9.875

Combine like terms: 9.875 + -9.875 = 0.000
0.000 + x = -9.670347719 + -9.875
x = -9.670347719 + -9.875

Combine like terms: -9.670347719 + -9.875 = -19.545347719
x = -19.545347719

Simplifying
x = -19.545347719


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.204652281, -19.545347719}

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