2x^2+17x-6.7=0

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Solution for 2x^2+17x-6.7=0 equation: 


Simplifying
2x2 + 17x + -6.7 = 0

Reorder the terms:
-6.7 + 17x + 2x2 = 0

Solving
-6.7 + 17x + 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'.
-3.35 + 8.5x + x2 = 0

Move the constant term to the right:

Add '3.35' to each side of the equation.
-3.35 + 8.5x + 3.35 + x2 = 0 + 3.35

Reorder the terms:
-3.35 + 3.35 + 8.5x + x2 = 0 + 3.35

Combine like terms: -3.35 + 3.35 = 0.00
0.00 + 8.5x + x2 = 0 + 3.35
8.5x + x2 = 0 + 3.35

Combine like terms: 0 + 3.35 = 3.35
8.5x + x2 = 3.35

The x term is 8.5x.  Take half its coefficient (4.25).
Square it (18.0625) and add it to both sides.

Add '18.0625' to each side of the equation.
8.5x + 18.0625 + x2 = 3.35 + 18.0625

Reorder the terms:
18.0625 + 8.5x + x2 = 3.35 + 18.0625

Combine like terms: 3.35 + 18.0625 = 21.4125
18.0625 + 8.5x + x2 = 21.4125

Factor a perfect square on the left side:
(x + 4.25)(x + 4.25) = 21.4125

Calculate the square root of the right side: 4.627364261

Break this problem into two subproblems by setting 
(x + 4.25) equal to 4.627364261 and -4.627364261.


Subproblem 1
x + 4.25 = 4.627364261

Simplifying
x + 4.25 = 4.627364261

Reorder the terms:
4.25 + x = 4.627364261

Solving
4.25 + x = 4.627364261

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = 4.627364261 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = 4.627364261 + -4.25
x = 4.627364261 + -4.25

Combine like terms: 4.627364261 + -4.25 = 0.377364261
x = 0.377364261

Simplifying
x = 0.377364261


Subproblem 2
x + 4.25 = -4.627364261

Simplifying
x + 4.25 = -4.627364261

Reorder the terms:
4.25 + x = -4.627364261

Solving
4.25 + x = -4.627364261

Solving for variable 'x'.

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

Add '-4.25' to each side of the equation.
4.25 + -4.25 + x = -4.627364261 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + x = -4.627364261 + -4.25
x = -4.627364261 + -4.25

Combine like terms: -4.627364261 + -4.25 = -8.877364261
x = -8.877364261

Simplifying
x = -8.877364261


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.377364261, -8.877364261}

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