3x^2-75x+100=0

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Solution for 3x^2-75x+100=0 equation:


Simplifying
3x2 + -75x + 100 = 0

Reorder the terms:
100 + -75x + 3x2 = 0

Solving
100 + -75x + 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'.
33.33333333 + -25x + x2 = 0

Move the constant term to the right:

Add '-33.33333333' to each side of the equation.
33.33333333 + -25x + -33.33333333 + x2 = 0 + -33.33333333

Reorder the terms:
33.33333333 + -33.33333333 + -25x + x2 = 0 + -33.33333333

Combine like terms: 33.33333333 + -33.33333333 = 0.00000000
0.00000000 + -25x + x2 = 0 + -33.33333333
-25x + x2 = 0 + -33.33333333

Combine like terms: 0 + -33.33333333 = -33.33333333
-25x + x2 = -33.33333333

The x term is -25x.  Take half its coefficient (-12.5).
Square it (156.25) and add it to both sides.

Add '156.25' to each side of the equation.
-25x + 156.25 + x2 = -33.33333333 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -33.33333333 + 156.25

Combine like terms: -33.33333333 + 156.25 = 122.91666667
156.25 + -25x + x2 = 122.91666667

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 122.91666667

Calculate the square root of the right side: 11.086778913

Break this problem into two subproblems by setting 
(x + -12.5) equal to 11.086778913 and -11.086778913.

Subproblem 1

x + -12.5 = 11.086778913 Simplifying x + -12.5 = 11.086778913 Reorder the terms: -12.5 + x = 11.086778913 Solving -12.5 + x = 11.086778913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = 11.086778913 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.086778913 + 12.5 x = 11.086778913 + 12.5 Combine like terms: 11.086778913 + 12.5 = 23.586778913 x = 23.586778913 Simplifying x = 23.586778913

Subproblem 2

x + -12.5 = -11.086778913 Simplifying x + -12.5 = -11.086778913 Reorder the terms: -12.5 + x = -11.086778913 Solving -12.5 + x = -11.086778913 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.5' to each side of the equation. -12.5 + 12.5 + x = -11.086778913 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.086778913 + 12.5 x = -11.086778913 + 12.5 Combine like terms: -11.086778913 + 12.5 = 1.413221087 x = 1.413221087 Simplifying x = 1.413221087

Solution

The solution to the problem is based on the solutions from the subproblems. x = {23.586778913, 1.413221087}

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