4x^2-17x-4=0

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


Simplifying
4x2 + -17x + -4 = 0

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

Solving
-4 + -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'.
-1 + -4.25x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4.25x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4.25x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4.25x + x2 = 0 + 1
-4.25x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-4.25x + x2 = 1

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 = 1 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = 1 + 4.515625

Combine like terms: 1 + 4.515625 = 5.515625
4.515625 + -4.25x + x2 = 5.515625

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 5.515625

Calculate the square root of the right side: 2.348536779

Break this problem into two subproblems by setting 
(x + -2.125) equal to 2.348536779 and -2.348536779.


Subproblem 1
x + -2.125 = 2.348536779

Simplifying
x + -2.125 = 2.348536779

Reorder the terms:
-2.125 + x = 2.348536779

Solving
-2.125 + x = 2.348536779

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 = 2.348536779 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = 2.348536779 + 2.125
x = 2.348536779 + 2.125

Combine like terms: 2.348536779 + 2.125 = 4.473536779
x = 4.473536779

Simplifying
x = 4.473536779


Subproblem 2
x + -2.125 = -2.348536779

Simplifying
x + -2.125 = -2.348536779

Reorder the terms:
-2.125 + x = -2.348536779

Solving
-2.125 + x = -2.348536779

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 = -2.348536779 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = -2.348536779 + 2.125
x = -2.348536779 + 2.125

Combine like terms: -2.348536779 + 2.125 = -0.223536779
x = -0.223536779

Simplifying
x = -0.223536779


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.473536779, -0.223536779}

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