x+x(2x-7)=44

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Solution for x+x(2x-7)=44 equation: 


Simplifying
x + x(2x + -7) = 44

Reorder the terms:
x + x(-7 + 2x) = 44
x + (-7 * x + 2x * x) = 44
x + (-7x + 2x2) = 44

Combine like terms: x + -7x = -6x
-6x + 2x2 = 44

Solving
-6x + 2x2 = 44

Solving for variable 'x'.

Reorder the terms:
-44 + -6x + 2x2 = 44 + -44

Combine like terms: 44 + -44 = 0
-44 + -6x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-22 + -3x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-22 + -3x + x2)' equal to zero and attempt to solve:

Simplifying
-22 + -3x + x2 = 0

Solving
-22 + -3x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -3x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -3x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -3x + x2 = 0 + 22
-3x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-3x + x2 = 22

The x term is -3x.  Take half its coefficient (-1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
-3x + 2.25 + x2 = 22 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 22 + 2.25

Combine like terms: 22 + 2.25 = 24.25
2.25 + -3x + x2 = 24.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 24.25

Calculate the square root of the right side: 4.924428901

Break this problem into two subproblems by setting 
(x + -1.5) equal to 4.924428901 and -4.924428901.


Subproblem 1
x + -1.5 = 4.924428901

Simplifying
x + -1.5 = 4.924428901

Reorder the terms:
-1.5 + x = 4.924428901

Solving
-1.5 + x = 4.924428901

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = 4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = 4.924428901 + 1.5
x = 4.924428901 + 1.5

Combine like terms: 4.924428901 + 1.5 = 6.424428901
x = 6.424428901

Simplifying
x = 6.424428901


Subproblem 2
x + -1.5 = -4.924428901

Simplifying
x + -1.5 = -4.924428901

Reorder the terms:
-1.5 + x = -4.924428901

Solving
-1.5 + x = -4.924428901

Solving for variable 'x'.

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

Add '1.5' to each side of the equation.
-1.5 + 1.5 + x = -4.924428901 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + x = -4.924428901 + 1.5
x = -4.924428901 + 1.5

Combine like terms: -4.924428901 + 1.5 = -3.424428901
x = -3.424428901

Simplifying
x = -3.424428901


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.424428901, -3.424428901}
Solution
x = {6.424428901, -3.424428901}

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