(2x)+(x+14)+(x-38)x=

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Solution for (2x)+(x+14)+(x-38)x= equation:


Simplifying
(2x) + (x + 14) + (x + -38) * x = 0

Reorder the terms:
(2x) + (14 + x) + (x + -38) * x = 0

Remove parenthesis around (14 + x)
(2x) + 14 + x + (x + -38) * x = 0

Reorder the terms:
(2x) + 14 + x + (-38 + x) * x = 0

Reorder the terms for easier multiplication:
(2x) + 14 + x + x(-38 + x) = 0
(2x) + 14 + x + (-38 * x + x * x) = 0
(2x) + 14 + x + (-38x + x2) = 0

Reorder the terms:
14 + (2x) + x + -38x + x2 = 0

Combine like terms: (2x) + x = 3x
14 + 3x + -38x + x2 = 0

Combine like terms: 3x + -38x = -35x
14 + -35x + x2 = 0

Solving
14 + -35x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-14' to each side of the equation.
14 + -35x + -14 + x2 = 0 + -14

Reorder the terms:
14 + -14 + -35x + x2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -35x + x2 = 0 + -14
-35x + x2 = 0 + -14

Combine like terms: 0 + -14 = -14
-35x + x2 = -14

The x term is -35x.  Take half its coefficient (-17.5).
Square it (306.25) and add it to both sides.

Add '306.25' to each side of the equation.
-35x + 306.25 + x2 = -14 + 306.25

Reorder the terms:
306.25 + -35x + x2 = -14 + 306.25

Combine like terms: -14 + 306.25 = 292.25
306.25 + -35x + x2 = 292.25

Factor a perfect square on the left side:
(x + -17.5)(x + -17.5) = 292.25

Calculate the square root of the right side: 17.095320997

Break this problem into two subproblems by setting 
(x + -17.5) equal to 17.095320997 and -17.095320997.

Subproblem 1

x + -17.5 = 17.095320997 Simplifying x + -17.5 = 17.095320997 Reorder the terms: -17.5 + x = 17.095320997 Solving -17.5 + x = 17.095320997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = 17.095320997 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = 17.095320997 + 17.5 x = 17.095320997 + 17.5 Combine like terms: 17.095320997 + 17.5 = 34.595320997 x = 34.595320997 Simplifying x = 34.595320997

Subproblem 2

x + -17.5 = -17.095320997 Simplifying x + -17.5 = -17.095320997 Reorder the terms: -17.5 + x = -17.095320997 Solving -17.5 + x = -17.095320997 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17.5' to each side of the equation. -17.5 + 17.5 + x = -17.095320997 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + x = -17.095320997 + 17.5 x = -17.095320997 + 17.5 Combine like terms: -17.095320997 + 17.5 = 0.404679003 x = 0.404679003 Simplifying x = 0.404679003

Solution

The solution to the problem is based on the solutions from the subproblems. x = {34.595320997, 0.404679003}

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