3x^2-69x+28=0

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Solution for 3x^2-69x+28=0 equation:


Simplifying
3x2 + -69x + 28 = 0

Reorder the terms:
28 + -69x + 3x2 = 0

Solving
28 + -69x + 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'.
9.333333333 + -23x + x2 = 0

Move the constant term to the right:

Add '-9.333333333' to each side of the equation.
9.333333333 + -23x + -9.333333333 + x2 = 0 + -9.333333333

Reorder the terms:
9.333333333 + -9.333333333 + -23x + x2 = 0 + -9.333333333

Combine like terms: 9.333333333 + -9.333333333 = 0.000000000
0.000000000 + -23x + x2 = 0 + -9.333333333
-23x + x2 = 0 + -9.333333333

Combine like terms: 0 + -9.333333333 = -9.333333333
-23x + x2 = -9.333333333

The x term is -23x.  Take half its coefficient (-11.5).
Square it (132.25) and add it to both sides.

Add '132.25' to each side of the equation.
-23x + 132.25 + x2 = -9.333333333 + 132.25

Reorder the terms:
132.25 + -23x + x2 = -9.333333333 + 132.25

Combine like terms: -9.333333333 + 132.25 = 122.916666667
132.25 + -23x + x2 = 122.916666667

Factor a perfect square on the left side:
(x + -11.5)(x + -11.5) = 122.916666667

Calculate the square root of the right side: 11.086778913

Break this problem into two subproblems by setting 
(x + -11.5) equal to 11.086778913 and -11.086778913.

Subproblem 1

x + -11.5 = 11.086778913 Simplifying x + -11.5 = 11.086778913 Reorder the terms: -11.5 + x = 11.086778913 Solving -11.5 + x = 11.086778913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = 11.086778913 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = 11.086778913 + 11.5 x = 11.086778913 + 11.5 Combine like terms: 11.086778913 + 11.5 = 22.586778913 x = 22.586778913 Simplifying x = 22.586778913

Subproblem 2

x + -11.5 = -11.086778913 Simplifying x + -11.5 = -11.086778913 Reorder the terms: -11.5 + x = -11.086778913 Solving -11.5 + x = -11.086778913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '11.5' to each side of the equation. -11.5 + 11.5 + x = -11.086778913 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + x = -11.086778913 + 11.5 x = -11.086778913 + 11.5 Combine like terms: -11.086778913 + 11.5 = 0.413221087 x = 0.413221087 Simplifying x = 0.413221087

Solution

The solution to the problem is based on the solutions from the subproblems. x = {22.586778913, 0.413221087}

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