2x^2+8x+17=-33-20x

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Solution for 2x^2+8x+17=-33-20x equation: 


Simplifying
2x2 + 8x + 17 = -33 + -20x

Reorder the terms:
17 + 8x + 2x2 = -33 + -20x

Solving
17 + 8x + 2x2 = -33 + -20x

Solving for variable 'x'.

Reorder the terms:
17 + 33 + 8x + 20x + 2x2 = -33 + -20x + 33 + 20x

Combine like terms: 17 + 33 = 50
50 + 8x + 20x + 2x2 = -33 + -20x + 33 + 20x

Combine like terms: 8x + 20x = 28x
50 + 28x + 2x2 = -33 + -20x + 33 + 20x

Reorder the terms:
50 + 28x + 2x2 = -33 + 33 + -20x + 20x

Combine like terms: -33 + 33 = 0
50 + 28x + 2x2 = 0 + -20x + 20x
50 + 28x + 2x2 = -20x + 20x

Combine like terms: -20x + 20x = 0
50 + 28x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(25 + 14x + x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(25 + 14x + x2)' equal to zero and attempt to solve:

Simplifying
25 + 14x + x2 = 0

Solving
25 + 14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-25' to each side of the equation.
25 + 14x + -25 + x2 = 0 + -25

Reorder the terms:
25 + -25 + 14x + x2 = 0 + -25

Combine like terms: 25 + -25 = 0
0 + 14x + x2 = 0 + -25
14x + x2 = 0 + -25

Combine like terms: 0 + -25 = -25
14x + x2 = -25

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 = -25 + 49

Reorder the terms:
49 + 14x + x2 = -25 + 49

Combine like terms: -25 + 49 = 24
49 + 14x + x2 = 24

Factor a perfect square on the left side:
(x + 7)(x + 7) = 24

Calculate the square root of the right side: 4.898979486

Break this problem into two subproblems by setting 
(x + 7) equal to 4.898979486 and -4.898979486.


Subproblem 1
x + 7 = 4.898979486

Simplifying
x + 7 = 4.898979486

Reorder the terms:
7 + x = 4.898979486

Solving
7 + x = 4.898979486

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 = 4.898979486 + -7

Combine like terms: 7 + -7 = 0
0 + x = 4.898979486 + -7
x = 4.898979486 + -7

Combine like terms: 4.898979486 + -7 = -2.101020514
x = -2.101020514

Simplifying
x = -2.101020514


Subproblem 2
x + 7 = -4.898979486

Simplifying
x + 7 = -4.898979486

Reorder the terms:
7 + x = -4.898979486

Solving
7 + x = -4.898979486

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 = -4.898979486 + -7

Combine like terms: 7 + -7 = 0
0 + x = -4.898979486 + -7
x = -4.898979486 + -7

Combine like terms: -4.898979486 + -7 = -11.898979486
x = -11.898979486

Simplifying
x = -11.898979486


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-2.101020514, -11.898979486}
Solution
x = {-2.101020514, -11.898979486}

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