7=2x+x^2+3(4x)+17

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Solution for 7=2x+x^2+3(4x)+17 equation: 


Simplifying
7 = 2x + x2 + 3(4x) + 17

Remove parenthesis around (4x)
7 = 2x + x2 + 3 * 4x + 17

Multiply 3 * 4
7 = 2x + x2 + 12x + 17

Reorder the terms:
7 = 17 + 2x + 12x + x2

Combine like terms: 2x + 12x = 14x
7 = 17 + 14x + x2

Solving
7 = 17 + 14x + x2

Solving for variable 'x'.

Combine like terms: 7 + -17 = -10
-10 + -14x + -1x2 = 17 + 14x + x2 + -17 + -14x + -1x2

Reorder the terms:
-10 + -14x + -1x2 = 17 + -17 + 14x + -14x + x2 + -1x2

Combine like terms: 17 + -17 = 0
-10 + -14x + -1x2 = 0 + 14x + -14x + x2 + -1x2
-10 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
-10 + -14x + -1x2 = 0 + x2 + -1x2
-10 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + -14x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(10 + 14x + x2) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(10 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
10 + 14x + x2 = 0

Solving
10 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-10' to each side of the equation.
10 + 14x + -10 + x2 = 0 + -10

Reorder the terms:
10 + -10 + 14x + x2 = 0 + -10

Combine like terms: 10 + -10 = 0
0 + 14x + x2 = 0 + -10
14x + x2 = 0 + -10

Combine like terms: 0 + -10 = -10
14x + x2 = -10

The x term is 14x.  Take half its coefficient (7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
14x + 49 + x2 = -10 + 49

Reorder the terms:
49 + 14x + x2 = -10 + 49

Combine like terms: -10 + 49 = 39
49 + 14x + x2 = 39

Factor a perfect square on the left side:
(x + 7)(x + 7) = 39

Calculate the square root of the right side: 6.244997998

Break this problem into two subproblems by setting 
(x + 7) equal to 6.244997998 and -6.244997998.


Subproblem 1
x + 7 = 6.244997998

Simplifying
x + 7 = 6.244997998

Reorder the terms:
7 + x = 6.244997998

Solving
7 + x = 6.244997998

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = 6.244997998 + -7

Combine like terms: 7 + -7 = 0
0 + x = 6.244997998 + -7
x = 6.244997998 + -7

Combine like terms: 6.244997998 + -7 = -0.755002002
x = -0.755002002

Simplifying
x = -0.755002002


Subproblem 2
x + 7 = -6.244997998

Simplifying
x + 7 = -6.244997998

Reorder the terms:
7 + x = -6.244997998

Solving
7 + x = -6.244997998

Solving for variable 'x'.

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

Add '-7' to each side of the equation.
7 + -7 + x = -6.244997998 + -7

Combine like terms: 7 + -7 = 0
0 + x = -6.244997998 + -7
x = -6.244997998 + -7

Combine like terms: -6.244997998 + -7 = -13.244997998
x = -13.244997998

Simplifying
x = -13.244997998


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.755002002, -13.244997998}
Solution
x = {-0.755002002, -13.244997998}

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