3x^2-75x+44=0

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Solution for 3x^2-75x+44=0 equation:


Simplifying
3x2 + -75x + 44 = 0

Reorder the terms:
44 + -75x + 3x2 = 0

Solving
44 + -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'.
14.66666667 + -25x + x2 = 0

Move the constant term to the right:

Add '-14.66666667' to each side of the equation.
14.66666667 + -25x + -14.66666667 + x2 = 0 + -14.66666667

Reorder the terms:
14.66666667 + -14.66666667 + -25x + x2 = 0 + -14.66666667

Combine like terms: 14.66666667 + -14.66666667 = 0.00000000
0.00000000 + -25x + x2 = 0 + -14.66666667
-25x + x2 = 0 + -14.66666667

Combine like terms: 0 + -14.66666667 = -14.66666667
-25x + x2 = -14.66666667

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 = -14.66666667 + 156.25

Reorder the terms:
156.25 + -25x + x2 = -14.66666667 + 156.25

Combine like terms: -14.66666667 + 156.25 = 141.58333333
156.25 + -25x + x2 = 141.58333333

Factor a perfect square on the left side:
(x + -12.5)(x + -12.5) = 141.58333333

Calculate the square root of the right side: 11.898879499

Break this problem into two subproblems by setting 
(x + -12.5) equal to 11.898879499 and -11.898879499.

Subproblem 1

x + -12.5 = 11.898879499 Simplifying x + -12.5 = 11.898879499 Reorder the terms: -12.5 + x = 11.898879499 Solving -12.5 + x = 11.898879499 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 = 11.898879499 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = 11.898879499 + 12.5 x = 11.898879499 + 12.5 Combine like terms: 11.898879499 + 12.5 = 24.398879499 x = 24.398879499 Simplifying x = 24.398879499

Subproblem 2

x + -12.5 = -11.898879499 Simplifying x + -12.5 = -11.898879499 Reorder the terms: -12.5 + x = -11.898879499 Solving -12.5 + x = -11.898879499 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 = -11.898879499 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + x = -11.898879499 + 12.5 x = -11.898879499 + 12.5 Combine like terms: -11.898879499 + 12.5 = 0.601120501 x = 0.601120501 Simplifying x = 0.601120501

Solution

The solution to the problem is based on the solutions from the subproblems. x = {24.398879499, 0.601120501}

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