170=x(2x+1)+(3x+2)

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Solution for 170=x(2x+1)+(3x+2) equation: 


Simplifying
170 = x(2x + 1) + (3x + 2)

Reorder the terms:
170 = x(1 + 2x) + (3x + 2)
170 = (1 * x + 2x * x) + (3x + 2)
170 = (1x + 2x2) + (3x + 2)

Reorder the terms:
170 = 1x + 2x2 + (2 + 3x)

Remove parenthesis around (2 + 3x)
170 = 1x + 2x2 + 2 + 3x

Reorder the terms:
170 = 2 + 1x + 3x + 2x2

Combine like terms: 1x + 3x = 4x
170 = 2 + 4x + 2x2

Solving
170 = 2 + 4x + 2x2

Solving for variable 'x'.

Combine like terms: 170 + -2 = 168
168 + -4x + -2x2 = 2 + 4x + 2x2 + -2 + -4x + -2x2

Reorder the terms:
168 + -4x + -2x2 = 2 + -2 + 4x + -4x + 2x2 + -2x2

Combine like terms: 2 + -2 = 0
168 + -4x + -2x2 = 0 + 4x + -4x + 2x2 + -2x2
168 + -4x + -2x2 = 4x + -4x + 2x2 + -2x2

Combine like terms: 4x + -4x = 0
168 + -4x + -2x2 = 0 + 2x2 + -2x2
168 + -4x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
168 + -4x + -2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(84 + -2x + -1x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(84 + -2x + -1x2)' equal to zero and attempt to solve:

Simplifying
84 + -2x + -1x2 = 0

Solving
84 + -2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-84 + 2x + x2 = 0

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + 2x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + 2x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + 2x + x2 = 0 + 84
2x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
2x + x2 = 84

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 84 + 1

Reorder the terms:
1 + 2x + x2 = 84 + 1

Combine like terms: 84 + 1 = 85
1 + 2x + x2 = 85

Factor a perfect square on the left side:
(x + 1)(x + 1) = 85

Calculate the square root of the right side: 9.219544457

Break this problem into two subproblems by setting 
(x + 1) equal to 9.219544457 and -9.219544457.


Subproblem 1
x + 1 = 9.219544457

Simplifying
x + 1 = 9.219544457

Reorder the terms:
1 + x = 9.219544457

Solving
1 + x = 9.219544457

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 9.219544457 + -1

Combine like terms: 1 + -1 = 0
0 + x = 9.219544457 + -1
x = 9.219544457 + -1

Combine like terms: 9.219544457 + -1 = 8.219544457
x = 8.219544457

Simplifying
x = 8.219544457


Subproblem 2
x + 1 = -9.219544457

Simplifying
x + 1 = -9.219544457

Reorder the terms:
1 + x = -9.219544457

Solving
1 + x = -9.219544457

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -9.219544457 + -1

Combine like terms: 1 + -1 = 0
0 + x = -9.219544457 + -1
x = -9.219544457 + -1

Combine like terms: -9.219544457 + -1 = -10.219544457
x = -10.219544457

Simplifying
x = -10.219544457


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.219544457, -10.219544457}
Solution
x = {8.219544457, -10.219544457}

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