4x^2+44x+88=0

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Solution for 4x^2+44x+88=0 equation:


Simplifying
4x2 + 44x + 88 = 0

Reorder the terms:
88 + 44x + 4x2 = 0

Solving
88 + 44x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(22 + 11x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(22 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
22 + 11x + x2 = 0

Solving
22 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-22' to each side of the equation.
22 + 11x + -22 + x2 = 0 + -22

Reorder the terms:
22 + -22 + 11x + x2 = 0 + -22

Combine like terms: 22 + -22 = 0
0 + 11x + x2 = 0 + -22
11x + x2 = 0 + -22

Combine like terms: 0 + -22 = -22
11x + x2 = -22

The x term is 11x.  Take half its coefficient (5.5).
Square it (30.25) and add it to both sides.

Add '30.25' to each side of the equation.
11x + 30.25 + x2 = -22 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -22 + 30.25

Combine like terms: -22 + 30.25 = 8.25
30.25 + 11x + x2 = 8.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 8.25

Calculate the square root of the right side: 2.872281323

Break this problem into two subproblems by setting 
(x + 5.5) equal to 2.872281323 and -2.872281323.


Subproblem 1
x + 5.5 = 2.872281323

Simplifying
x + 5.5 = 2.872281323

Reorder the terms:
5.5 + x = 2.872281323

Solving
5.5 + x = 2.872281323

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = 2.872281323 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 2.872281323 + -5.5
x = 2.872281323 + -5.5

Combine like terms: 2.872281323 + -5.5 = -2.627718677
x = -2.627718677

Simplifying
x = -2.627718677


Subproblem 2
x + 5.5 = -2.872281323

Simplifying
x + 5.5 = -2.872281323

Reorder the terms:
5.5 + x = -2.872281323

Solving
5.5 + x = -2.872281323

Solving for variable 'x'.

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

Add '-5.5' to each side of the equation.
5.5 + -5.5 + x = -2.872281323 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -2.872281323 + -5.5
x = -2.872281323 + -5.5

Combine like terms: -2.872281323 + -5.5 = -8.372281323
x = -8.372281323

Simplifying
x = -8.372281323


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.627718677, -8.372281323}
Solution
x = {-2.627718677, -8.372281323}

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