4x^2+17x+17=0

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Solution for 4x^2+17x+17=0 equation: 


Simplifying
4x2 + 17x + 17 = 0

Reorder the terms:
17 + 17x + 4x2 = 0

Solving
17 + 17x + 4x2 = 0

Solving for variable 'x'.

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

Divide each side by '4'.
4.25 + 4.25x + x2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + 4.25x + -4.25 + x2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + 4.25x + x2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + 4.25x + x2 = 0 + -4.25
4.25x + x2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
4.25x + x2 = -4.25

The x term is 4.25x.  Take half its coefficient (2.125).
Square it (4.515625) and add it to both sides.

Add '4.515625' to each side of the equation.
4.25x + 4.515625 + x2 = -4.25 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = -4.25 + 4.515625

Combine like terms: -4.25 + 4.515625 = 0.265625
4.515625 + 4.25x + x2 = 0.265625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + 2.125) equal to 0.515388203 and -0.515388203.


Subproblem 1
x + 2.125 = 0.515388203

Simplifying
x + 2.125 = 0.515388203

Reorder the terms:
2.125 + x = 0.515388203

Solving
2.125 + x = 0.515388203

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = 0.515388203 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 0.515388203 + -2.125
x = 0.515388203 + -2.125

Combine like terms: 0.515388203 + -2.125 = -1.609611797
x = -1.609611797

Simplifying
x = -1.609611797


Subproblem 2
x + 2.125 = -0.515388203

Simplifying
x + 2.125 = -0.515388203

Reorder the terms:
2.125 + x = -0.515388203

Solving
2.125 + x = -0.515388203

Solving for variable 'x'.

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

Add '-2.125' to each side of the equation.
2.125 + -2.125 + x = -0.515388203 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -0.515388203 + -2.125
x = -0.515388203 + -2.125

Combine like terms: -0.515388203 + -2.125 = -2.640388203
x = -2.640388203

Simplifying
x = -2.640388203


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.609611797, -2.640388203}

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