4X^2+48X+92=0

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Solution for 4X^2+48X+92=0 equation: 


Simplifying
4X2 + 48X + 92 = 0

Reorder the terms:
92 + 48X + 4X2 = 0

Solving
92 + 48X + 4X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), '4'.
4(23 + 12X + X2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(23 + 12X + X2)' equal to zero and attempt to solve:

Simplifying
23 + 12X + X2 = 0

Solving
23 + 12X + X2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-23' to each side of the equation.
23 + 12X + -23 + X2 = 0 + -23

Reorder the terms:
23 + -23 + 12X + X2 = 0 + -23

Combine like terms: 23 + -23 = 0
0 + 12X + X2 = 0 + -23
12X + X2 = 0 + -23

Combine like terms: 0 + -23 = -23
12X + X2 = -23

The X term is 12X.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12X + 36 + X2 = -23 + 36

Reorder the terms:
36 + 12X + X2 = -23 + 36

Combine like terms: -23 + 36 = 13
36 + 12X + X2 = 13

Factor a perfect square on the left side:
(X + 6)(X + 6) = 13

Calculate the square root of the right side: 3.605551275

Break this problem into two subproblems by setting 
(X + 6) equal to 3.605551275 and -3.605551275.


Subproblem 1
X + 6 = 3.605551275

Simplifying
X + 6 = 3.605551275

Reorder the terms:
6 + X = 3.605551275

Solving
6 + X = 3.605551275

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + -6 + X = 3.605551275 + -6

Combine like terms: 6 + -6 = 0
0 + X = 3.605551275 + -6
X = 3.605551275 + -6

Combine like terms: 3.605551275 + -6 = -2.394448725
X = -2.394448725

Simplifying
X = -2.394448725


Subproblem 2
X + 6 = -3.605551275

Simplifying
X + 6 = -3.605551275

Reorder the terms:
6 + X = -3.605551275

Solving
6 + X = -3.605551275

Solving for variable 'X'.

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

Add '-6' to each side of the equation.
6 + -6 + X = -3.605551275 + -6

Combine like terms: 6 + -6 = 0
0 + X = -3.605551275 + -6
X = -3.605551275 + -6

Combine like terms: -3.605551275 + -6 = -9.605551275
X = -9.605551275

Simplifying
X = -9.605551275


Solution
The solution to the problem is based on the solutions
from the subproblems.
X = {-2.394448725, -9.605551275}
Solution
X = {-2.394448725, -9.605551275}

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