4x^2+41x+98=-2-3x

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Solution for 4x^2+41x+98=-2-3x equation: 


Simplifying
4x2 + 41x + 98 = -2 + -3x

Reorder the terms:
98 + 41x + 4x2 = -2 + -3x

Solving
98 + 41x + 4x2 = -2 + -3x

Solving for variable 'x'.

Reorder the terms:
98 + 2 + 41x + 3x + 4x2 = -2 + -3x + 2 + 3x

Combine like terms: 98 + 2 = 100
100 + 41x + 3x + 4x2 = -2 + -3x + 2 + 3x

Combine like terms: 41x + 3x = 44x
100 + 44x + 4x2 = -2 + -3x + 2 + 3x

Reorder the terms:
100 + 44x + 4x2 = -2 + 2 + -3x + 3x

Combine like terms: -2 + 2 = 0
100 + 44x + 4x2 = 0 + -3x + 3x
100 + 44x + 4x2 = -3x + 3x

Combine like terms: -3x + 3x = 0
100 + 44x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(25 + 11x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(25 + 11x + x2)' equal to zero and attempt to solve:

Simplifying
25 + 11x + x2 = 0

Solving
25 + 11x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 11x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 11x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 11x + x2 = 0 + -25
11x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
11x + x2 = -25

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 = -25 + 30.25

Reorder the terms:
30.25 + 11x + x2 = -25 + 30.25

Combine like terms: -25 + 30.25 = 5.25
30.25 + 11x + x2 = 5.25

Factor a perfect square on the left side:
(x + 5.5)(x + 5.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 5.5) equal to 2.291287847 and -2.291287847.


Subproblem 1
x + 5.5 = 2.291287847

Simplifying
x + 5.5 = 2.291287847

Reorder the terms:
5.5 + x = 2.291287847

Solving
5.5 + x = 2.291287847

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 = 2.291287847 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = 2.291287847 + -5.5
x = 2.291287847 + -5.5

Combine like terms: 2.291287847 + -5.5 = -3.208712153
x = -3.208712153

Simplifying
x = -3.208712153


Subproblem 2
x + 5.5 = -2.291287847

Simplifying
x + 5.5 = -2.291287847

Reorder the terms:
5.5 + x = -2.291287847

Solving
5.5 + x = -2.291287847

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 = -2.291287847 + -5.5

Combine like terms: 5.5 + -5.5 = 0.0
0.0 + x = -2.291287847 + -5.5
x = -2.291287847 + -5.5

Combine like terms: -2.291287847 + -5.5 = -7.791287847
x = -7.791287847

Simplifying
x = -7.791287847


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.208712153, -7.791287847}
Solution
x = {-3.208712153, -7.791287847}

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