4x^2-25x+17=0

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Solution for 4x^2-25x+17=0 equation: 


Simplifying
4x2 + -25x + 17 = 0

Reorder the terms:
17 + -25x + 4x2 = 0

Solving
17 + -25x + 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 + -6.25x + x2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + -6.25x + -4.25 + x2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + -6.25x + x2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + -6.25x + x2 = 0 + -4.25
-6.25x + x2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
-6.25x + x2 = -4.25

The x term is -6.25x.  Take half its coefficient (-3.125).
Square it (9.765625) and add it to both sides.

Add '9.765625' to each side of the equation.
-6.25x + 9.765625 + x2 = -4.25 + 9.765625

Reorder the terms:
9.765625 + -6.25x + x2 = -4.25 + 9.765625

Combine like terms: -4.25 + 9.765625 = 5.515625
9.765625 + -6.25x + x2 = 5.515625

Factor a perfect square on the left side:
(x + -3.125)(x + -3.125) = 5.515625

Calculate the square root of the right side: 2.348536779

Break this problem into two subproblems by setting 
(x + -3.125) equal to 2.348536779 and -2.348536779.


Subproblem 1
x + -3.125 = 2.348536779

Simplifying
x + -3.125 = 2.348536779

Reorder the terms:
-3.125 + x = 2.348536779

Solving
-3.125 + x = 2.348536779

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = 2.348536779 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = 2.348536779 + 3.125
x = 2.348536779 + 3.125

Combine like terms: 2.348536779 + 3.125 = 5.473536779
x = 5.473536779

Simplifying
x = 5.473536779


Subproblem 2
x + -3.125 = -2.348536779

Simplifying
x + -3.125 = -2.348536779

Reorder the terms:
-3.125 + x = -2.348536779

Solving
-3.125 + x = -2.348536779

Solving for variable 'x'.

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

Add '3.125' to each side of the equation.
-3.125 + 3.125 + x = -2.348536779 + 3.125

Combine like terms: -3.125 + 3.125 = 0.000
0.000 + x = -2.348536779 + 3.125
x = -2.348536779 + 3.125

Combine like terms: -2.348536779 + 3.125 = 0.776463221
x = 0.776463221

Simplifying
x = 0.776463221


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.473536779, 0.776463221}

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