4x^2+17x+1=0

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Solution for 4x^2+17x+1=0 equation: 


Simplifying
4x2 + 17x + 1 = 0

Reorder the terms:
1 + 17x + 4x2 = 0

Solving
1 + 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'.
0.25 + 4.25x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + 4.25x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + 4.25x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + 4.25x + x2 = 0 + -0.25
4.25x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
4.25x + x2 = -0.25

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 = -0.25 + 4.515625

Reorder the terms:
4.515625 + 4.25x + x2 = -0.25 + 4.515625

Combine like terms: -0.25 + 4.515625 = 4.265625
4.515625 + 4.25x + x2 = 4.265625

Factor a perfect square on the left side:
(x + 2.125)(x + 2.125) = 4.265625

Calculate the square root of the right side: 2.065338955

Break this problem into two subproblems by setting 
(x + 2.125) equal to 2.065338955 and -2.065338955.


Subproblem 1
x + 2.125 = 2.065338955

Simplifying
x + 2.125 = 2.065338955

Reorder the terms:
2.125 + x = 2.065338955

Solving
2.125 + x = 2.065338955

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 = 2.065338955 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = 2.065338955 + -2.125
x = 2.065338955 + -2.125

Combine like terms: 2.065338955 + -2.125 = -0.059661045
x = -0.059661045

Simplifying
x = -0.059661045


Subproblem 2
x + 2.125 = -2.065338955

Simplifying
x + 2.125 = -2.065338955

Reorder the terms:
2.125 + x = -2.065338955

Solving
2.125 + x = -2.065338955

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 = -2.065338955 + -2.125

Combine like terms: 2.125 + -2.125 = 0.000
0.000 + x = -2.065338955 + -2.125
x = -2.065338955 + -2.125

Combine like terms: -2.065338955 + -2.125 = -4.190338955
x = -4.190338955

Simplifying
x = -4.190338955


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.059661045, -4.190338955}

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