3x^2-29x+52=0

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Solution for 3x^2-29x+52=0 equation: 


Simplifying
3x2 + -29x + 52 = 0

Reorder the terms:
52 + -29x + 3x2 = 0

Solving
52 + -29x + 3x2 = 0

Solving for variable 'x'.

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

Divide each side by '3'.
17.33333333 + -9.666666667x + x2 = 0

Move the constant term to the right:

Add '-17.33333333' to each side of the equation.
17.33333333 + -9.666666667x + -17.33333333 + x2 = 0 + -17.33333333

Reorder the terms:
17.33333333 + -17.33333333 + -9.666666667x + x2 = 0 + -17.33333333

Combine like terms: 17.33333333 + -17.33333333 = 0.00000000
0.00000000 + -9.666666667x + x2 = 0 + -17.33333333
-9.666666667x + x2 = 0 + -17.33333333

Combine like terms: 0 + -17.33333333 = -17.33333333
-9.666666667x + x2 = -17.33333333

The x term is -9.666666667x.  Take half its coefficient (-4.833333334).
Square it (23.36111112) and add it to both sides.

Add '23.36111112' to each side of the equation.
-9.666666667x + 23.36111112 + x2 = -17.33333333 + 23.36111112

Reorder the terms:
23.36111112 + -9.666666667x + x2 = -17.33333333 + 23.36111112

Combine like terms: -17.33333333 + 23.36111112 = 6.02777779
23.36111112 + -9.666666667x + x2 = 6.02777779

Factor a perfect square on the left side:
(x + -4.833333334)(x + -4.833333334) = 6.02777779

Calculate the square root of the right side: 2.455153313

Break this problem into two subproblems by setting 
(x + -4.833333334) equal to 2.455153313 and -2.455153313.


Subproblem 1
x + -4.833333334 = 2.455153313

Simplifying
x + -4.833333334 = 2.455153313

Reorder the terms:
-4.833333334 + x = 2.455153313

Solving
-4.833333334 + x = 2.455153313

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = 2.455153313 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = 2.455153313 + 4.833333334
x = 2.455153313 + 4.833333334

Combine like terms: 2.455153313 + 4.833333334 = 7.288486647
x = 7.288486647

Simplifying
x = 7.288486647


Subproblem 2
x + -4.833333334 = -2.455153313

Simplifying
x + -4.833333334 = -2.455153313

Reorder the terms:
-4.833333334 + x = -2.455153313

Solving
-4.833333334 + x = -2.455153313

Solving for variable 'x'.

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

Add '4.833333334' to each side of the equation.
-4.833333334 + 4.833333334 + x = -2.455153313 + 4.833333334

Combine like terms: -4.833333334 + 4.833333334 = 0.000000000
0.000000000 + x = -2.455153313 + 4.833333334
x = -2.455153313 + 4.833333334

Combine like terms: -2.455153313 + 4.833333334 = 2.378180021
x = 2.378180021

Simplifying
x = 2.378180021


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.288486647, 2.378180021}

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