0=6x^2-50x+75

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Solution for 0=6x^2-50x+75 equation:


Simplifying
0 = 6x2 + -50x + 75

Reorder the terms:
0 = 75 + -50x + 6x2

Solving
0 = 75 + -50x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -75 = -75
-75 + 50x + -6x2 = 75 + -50x + 6x2 + -75 + 50x + -6x2

Reorder the terms:
-75 + 50x + -6x2 = 75 + -75 + -50x + 50x + 6x2 + -6x2

Combine like terms: 75 + -75 = 0
-75 + 50x + -6x2 = 0 + -50x + 50x + 6x2 + -6x2
-75 + 50x + -6x2 = -50x + 50x + 6x2 + -6x2

Combine like terms: -50x + 50x = 0
-75 + 50x + -6x2 = 0 + 6x2 + -6x2
-75 + 50x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-75 + 50x + -6x2 = 0

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
12.5 + -8.333333333x + x2 = 0

Move the constant term to the right:

Add '-12.5' to each side of the equation.
12.5 + -8.333333333x + -12.5 + x2 = 0 + -12.5

Reorder the terms:
12.5 + -12.5 + -8.333333333x + x2 = 0 + -12.5

Combine like terms: 12.5 + -12.5 = 0.0
0.0 + -8.333333333x + x2 = 0 + -12.5
-8.333333333x + x2 = 0 + -12.5

Combine like terms: 0 + -12.5 = -12.5
-8.333333333x + x2 = -12.5

The x term is -8.333333333x.  Take half its coefficient (-4.166666667).
Square it (17.36111111) and add it to both sides.

Add '17.36111111' to each side of the equation.
-8.333333333x + 17.36111111 + x2 = -12.5 + 17.36111111

Reorder the terms:
17.36111111 + -8.333333333x + x2 = -12.5 + 17.36111111

Combine like terms: -12.5 + 17.36111111 = 4.86111111
17.36111111 + -8.333333333x + x2 = 4.86111111

Factor a perfect square on the left side:
(x + -4.166666667)(x + -4.166666667) = 4.86111111

Calculate the square root of the right side: 2.204792759

Break this problem into two subproblems by setting 
(x + -4.166666667) equal to 2.204792759 and -2.204792759.

Subproblem 1

x + -4.166666667 = 2.204792759 Simplifying x + -4.166666667 = 2.204792759 Reorder the terms: -4.166666667 + x = 2.204792759 Solving -4.166666667 + x = 2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = 2.204792759 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = 2.204792759 + 4.166666667 x = 2.204792759 + 4.166666667 Combine like terms: 2.204792759 + 4.166666667 = 6.371459426 x = 6.371459426 Simplifying x = 6.371459426

Subproblem 2

x + -4.166666667 = -2.204792759 Simplifying x + -4.166666667 = -2.204792759 Reorder the terms: -4.166666667 + x = -2.204792759 Solving -4.166666667 + x = -2.204792759 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.166666667' to each side of the equation. -4.166666667 + 4.166666667 + x = -2.204792759 + 4.166666667 Combine like terms: -4.166666667 + 4.166666667 = 0.000000000 0.000000000 + x = -2.204792759 + 4.166666667 x = -2.204792759 + 4.166666667 Combine like terms: -2.204792759 + 4.166666667 = 1.961873908 x = 1.961873908 Simplifying x = 1.961873908

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.371459426, 1.961873908}

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