x(2x+5)+6x-17(3x+2)=

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Solution for x(2x+5)+6x-17(3x+2)= equation: 


Simplifying
x(2x + 5) + 6x + -17(3x + 2) = 0

Reorder the terms:
x(5 + 2x) + 6x + -17(3x + 2) = 0
(5 * x + 2x * x) + 6x + -17(3x + 2) = 0
(5x + 2x2) + 6x + -17(3x + 2) = 0

Reorder the terms:
5x + 2x2 + 6x + -17(2 + 3x) = 0
5x + 2x2 + 6x + (2 * -17 + 3x * -17) = 0
5x + 2x2 + 6x + (-34 + -51x) = 0

Reorder the terms:
-34 + 5x + 6x + -51x + 2x2 = 0

Combine like terms: 5x + 6x = 11x
-34 + 11x + -51x + 2x2 = 0

Combine like terms: 11x + -51x = -40x
-34 + -40x + 2x2 = 0

Solving
-34 + -40x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-17 + -20x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-17 + -20x + x2)' equal to zero and attempt to solve:

Simplifying
-17 + -20x + x2 = 0

Solving
-17 + -20x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '17' to each side of the equation.
-17 + -20x + 17 + x2 = 0 + 17

Reorder the terms:
-17 + 17 + -20x + x2 = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -20x + x2 = 0 + 17
-20x + x2 = 0 + 17

Combine like terms: 0 + 17 = 17
-20x + x2 = 17

The x term is -20x.  Take half its coefficient (-10).
Square it (100) and add it to both sides.

Add '100' to each side of the equation.
-20x + 100 + x2 = 17 + 100

Reorder the terms:
100 + -20x + x2 = 17 + 100

Combine like terms: 17 + 100 = 117
100 + -20x + x2 = 117

Factor a perfect square on the left side:
(x + -10)(x + -10) = 117

Calculate the square root of the right side: 10.816653826

Break this problem into two subproblems by setting 
(x + -10) equal to 10.816653826 and -10.816653826.


Subproblem 1
x + -10 = 10.816653826

Simplifying
x + -10 = 10.816653826

Reorder the terms:
-10 + x = 10.816653826

Solving
-10 + x = 10.816653826

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = 10.816653826 + 10

Combine like terms: -10 + 10 = 0
0 + x = 10.816653826 + 10
x = 10.816653826 + 10

Combine like terms: 10.816653826 + 10 = 20.816653826
x = 20.816653826

Simplifying
x = 20.816653826


Subproblem 2
x + -10 = -10.816653826

Simplifying
x + -10 = -10.816653826

Reorder the terms:
-10 + x = -10.816653826

Solving
-10 + x = -10.816653826

Solving for variable 'x'.

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

Add '10' to each side of the equation.
-10 + 10 + x = -10.816653826 + 10

Combine like terms: -10 + 10 = 0
0 + x = -10.816653826 + 10
x = -10.816653826 + 10

Combine like terms: -10.816653826 + 10 = -0.816653826
x = -0.816653826

Simplifying
x = -0.816653826


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {20.816653826, -0.816653826}
Solution
x = {20.816653826, -0.816653826}

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