8x^2-34x+29=0

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Solution for 8x^2-34x+29=0 equation: 


Simplifying
8x2 + -34x + 29 = 0

Reorder the terms:
29 + -34x + 8x2 = 0

Solving
29 + -34x + 8x2 = 0

Solving for variable 'x'.

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

Divide each side by '8'.
3.625 + -4.25x + x2 = 0

Move the constant term to the right:

Add '-3.625' to each side of the equation.
3.625 + -4.25x + -3.625 + x2 = 0 + -3.625

Reorder the terms:
3.625 + -3.625 + -4.25x + x2 = 0 + -3.625

Combine like terms: 3.625 + -3.625 = 0.000
0.000 + -4.25x + x2 = 0 + -3.625
-4.25x + x2 = 0 + -3.625

Combine like terms: 0 + -3.625 = -3.625
-4.25x + x2 = -3.625

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 = -3.625 + 4.515625

Reorder the terms:
4.515625 + -4.25x + x2 = -3.625 + 4.515625

Combine like terms: -3.625 + 4.515625 = 0.890625
4.515625 + -4.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + -2.125)(x + -2.125) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + -2.125) equal to 0.943729304 and -0.943729304.


Subproblem 1
x + -2.125 = 0.943729304

Simplifying
x + -2.125 = 0.943729304

Reorder the terms:
-2.125 + x = 0.943729304

Solving
-2.125 + x = 0.943729304

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 = 0.943729304 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = 0.943729304 + 2.125
x = 0.943729304 + 2.125

Combine like terms: 0.943729304 + 2.125 = 3.068729304
x = 3.068729304

Simplifying
x = 3.068729304


Subproblem 2
x + -2.125 = -0.943729304

Simplifying
x + -2.125 = -0.943729304

Reorder the terms:
-2.125 + x = -0.943729304

Solving
-2.125 + x = -0.943729304

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 = -0.943729304 + 2.125

Combine like terms: -2.125 + 2.125 = 0.000
0.000 + x = -0.943729304 + 2.125
x = -0.943729304 + 2.125

Combine like terms: -0.943729304 + 2.125 = 1.181270696
x = 1.181270696

Simplifying
x = 1.181270696


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.068729304, 1.181270696}

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