(4x^2+21x+24)=(x+4)

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Solution for (4x^2+21x+24)=(x+4) equation: 


Simplifying
(4x2 + 21x + 24) = (x + 4)

Reorder the terms:
(24 + 21x + 4x2) = (x + 4)

Remove parenthesis around (24 + 21x + 4x2)
24 + 21x + 4x2 = (x + 4)

Reorder the terms:
24 + 21x + 4x2 = (4 + x)

Remove parenthesis around (4 + x)
24 + 21x + 4x2 = 4 + x

Solving
24 + 21x + 4x2 = 4 + x

Solving for variable 'x'.

Reorder the terms:
24 + -4 + 21x + -1x + 4x2 = 4 + x + -4 + -1x

Combine like terms: 24 + -4 = 20
20 + 21x + -1x + 4x2 = 4 + x + -4 + -1x

Combine like terms: 21x + -1x = 20x
20 + 20x + 4x2 = 4 + x + -4 + -1x

Reorder the terms:
20 + 20x + 4x2 = 4 + -4 + x + -1x

Combine like terms: 4 + -4 = 0
20 + 20x + 4x2 = 0 + x + -1x
20 + 20x + 4x2 = x + -1x

Combine like terms: x + -1x = 0
20 + 20x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(5 + 5x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(5 + 5x + x2)' equal to zero and attempt to solve:

Simplifying
5 + 5x + x2 = 0

Solving
5 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-5' to each side of the equation.
5 + 5x + -5 + x2 = 0 + -5

Reorder the terms:
5 + -5 + 5x + x2 = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 5x + x2 = 0 + -5
5x + x2 = 0 + -5

Combine like terms: 0 + -5 = -5
5x + x2 = -5

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -5 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -5 + 6.25

Combine like terms: -5 + 6.25 = 1.25
6.25 + 5x + x2 = 1.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.118033989 and -1.118033989.


Subproblem 1
x + 2.5 = 1.118033989

Simplifying
x + 2.5 = 1.118033989

Reorder the terms:
2.5 + x = 1.118033989

Solving
2.5 + x = 1.118033989

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.118033989 + -2.5
x = 1.118033989 + -2.5

Combine like terms: 1.118033989 + -2.5 = -1.381966011
x = -1.381966011

Simplifying
x = -1.381966011


Subproblem 2
x + 2.5 = -1.118033989

Simplifying
x + 2.5 = -1.118033989

Reorder the terms:
2.5 + x = -1.118033989

Solving
2.5 + x = -1.118033989

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.118033989 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.118033989 + -2.5
x = -1.118033989 + -2.5

Combine like terms: -1.118033989 + -2.5 = -3.618033989
x = -3.618033989

Simplifying
x = -3.618033989


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.381966011, -3.618033989}
Solution
x = {-1.381966011, -3.618033989}

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