4x^2+56x+144=0

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Solution for 4x^2+56x+144=0 equation: 


Simplifying
4x2 + 56x + 144 = 0

Reorder the terms:
144 + 56x + 4x2 = 0

Solving
144 + 56x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(36 + 14x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(36 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
36 + 14x + x2 = 0

Solving
36 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-36' to each side of the equation.
36 + 14x + -36 + x2 = 0 + -36

Reorder the terms:
36 + -36 + 14x + x2 = 0 + -36

Combine like terms: 36 + -36 = 0
0 + 14x + x2 = 0 + -36
14x + x2 = 0 + -36

Combine like terms: 0 + -36 = -36
14x + x2 = -36

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -36 + 49

Reorder the terms:
49 + 14x + x2 = -36 + 49

Combine like terms: -36 + 49 = 13
49 + 14x + x2 = 13

Factor a perfect square on the left side:
(x + 7)(x + 7) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(x + 7) equal to 3.605551275 and -3.605551275.


Subproblem 1
x + 7 = 3.605551275

Simplifying
x + 7 = 3.605551275

Reorder the terms:
7 + x = 3.605551275

Solving
7 + x = 3.605551275

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 3.605551275 + -7

Combine like terms: 7 + -7 = 0
0 + x = 3.605551275 + -7
x = 3.605551275 + -7

Combine like terms: 3.605551275 + -7 = -3.394448725
x = -3.394448725

Simplifying
x = -3.394448725


Subproblem 2
x + 7 = -3.605551275

Simplifying
x + 7 = -3.605551275

Reorder the terms:
7 + x = -3.605551275

Solving
7 + x = -3.605551275

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -3.605551275 + -7

Combine like terms: 7 + -7 = 0
0 + x = -3.605551275 + -7
x = -3.605551275 + -7

Combine like terms: -3.605551275 + -7 = -10.605551275
x = -10.605551275

Simplifying
x = -10.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.394448725, -10.605551275}
Solution
x = {-3.394448725, -10.605551275}

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