2x^2+18x+17=0

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Solution for 2x^2+18x+17=0 equation:


Simplifying
2x2 + 18x + 17 = 0

Reorder the terms:
17 + 18x + 2x2 = 0

Solving
17 + 18x + 2x2 = 0

Solving for variable 'x'.

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

Divide each side by '2'.
8.5 + 9x + x2 = 0

Move the constant term to the right:

Add '-8.5' to each side of the equation.
8.5 + 9x + -8.5 + x2 = 0 + -8.5

Reorder the terms:
8.5 + -8.5 + 9x + x2 = 0 + -8.5

Combine like terms: 8.5 + -8.5 = 0.0
0.0 + 9x + x2 = 0 + -8.5
9x + x2 = 0 + -8.5

Combine like terms: 0 + -8.5 = -8.5
9x + x2 = -8.5

The x term is 9x.  Take half its coefficient (4.5).
Square it (20.25) and add it to both sides.

Add '20.25' to each side of the equation.
9x + 20.25 + x2 = -8.5 + 20.25

Reorder the terms:
20.25 + 9x + x2 = -8.5 + 20.25

Combine like terms: -8.5 + 20.25 = 11.75
20.25 + 9x + x2 = 11.75

Factor a perfect square on the left side:
(x + 4.5)(x + 4.5) = 11.75

Calculate the square root of the right side: 3.4278273

Break this problem into two subproblems by setting 
(x + 4.5) equal to 3.4278273 and -3.4278273.

Subproblem 1

x + 4.5 = 3.4278273 Simplifying x + 4.5 = 3.4278273 Reorder the terms: 4.5 + x = 3.4278273 Solving 4.5 + x = 3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 3.4278273 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 3.4278273 + -4.5 x = 3.4278273 + -4.5 Combine like terms: 3.4278273 + -4.5 = -1.0721727 x = -1.0721727 Simplifying x = -1.0721727

Subproblem 2

x + 4.5 = -3.4278273 Simplifying x + 4.5 = -3.4278273 Reorder the terms: 4.5 + x = -3.4278273 Solving 4.5 + x = -3.4278273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -3.4278273 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -3.4278273 + -4.5 x = -3.4278273 + -4.5 Combine like terms: -3.4278273 + -4.5 = -7.9278273 x = -7.9278273 Simplifying x = -7.9278273

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.0721727, -7.9278273}

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