4x^2-29x+17=0

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Solution for 4x^2-29x+17=0 equation: 


Simplifying
4x2 + -29x + 17 = 0

Reorder the terms:
17 + -29x + 4x2 = 0

Solving
17 + -29x + 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 + -7.25x + x2 = 0

Move the constant term to the right:

Add '-4.25' to each side of the equation.
4.25 + -7.25x + -4.25 + x2 = 0 + -4.25

Reorder the terms:
4.25 + -4.25 + -7.25x + x2 = 0 + -4.25

Combine like terms: 4.25 + -4.25 = 0.00
0.00 + -7.25x + x2 = 0 + -4.25
-7.25x + x2 = 0 + -4.25

Combine like terms: 0 + -4.25 = -4.25
-7.25x + x2 = -4.25

The x term is -7.25x.  Take half its coefficient (-3.625).
Square it (13.140625) and add it to both sides.

Add '13.140625' to each side of the equation.
-7.25x + 13.140625 + x2 = -4.25 + 13.140625

Reorder the terms:
13.140625 + -7.25x + x2 = -4.25 + 13.140625

Combine like terms: -4.25 + 13.140625 = 8.890625
13.140625 + -7.25x + x2 = 8.890625

Factor a perfect square on the left side:
(x + -3.625)(x + -3.625) = 8.890625

Calculate the square root of the right side: 2.98171511

Break this problem into two subproblems by setting 
(x + -3.625) equal to 2.98171511 and -2.98171511.


Subproblem 1
x + -3.625 = 2.98171511

Simplifying
x + -3.625 = 2.98171511

Reorder the terms:
-3.625 + x = 2.98171511

Solving
-3.625 + x = 2.98171511

Solving for variable 'x'.

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

Add '3.625' to each side of the equation.
-3.625 + 3.625 + x = 2.98171511 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + x = 2.98171511 + 3.625
x = 2.98171511 + 3.625

Combine like terms: 2.98171511 + 3.625 = 6.60671511
x = 6.60671511

Simplifying
x = 6.60671511


Subproblem 2
x + -3.625 = -2.98171511

Simplifying
x + -3.625 = -2.98171511

Reorder the terms:
-3.625 + x = -2.98171511

Solving
-3.625 + x = -2.98171511

Solving for variable 'x'.

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

Add '3.625' to each side of the equation.
-3.625 + 3.625 + x = -2.98171511 + 3.625

Combine like terms: -3.625 + 3.625 = 0.000
0.000 + x = -2.98171511 + 3.625
x = -2.98171511 + 3.625

Combine like terms: -2.98171511 + 3.625 = 0.64328489
x = 0.64328489

Simplifying
x = 0.64328489


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.60671511, 0.64328489}

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