7.5x^2-64989x+50000000=0

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Solution for 7.5x^2-64989x+50000000=0 equation: 


Simplifying
7.5x2 + -64989x + 50000000 = 0

Reorder the terms:
50000000 + -64989x + 7.5x2 = 0

Solving
50000000 + -64989x + 7.5x2 = 0

Solving for variable 'x'.

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

Divide each side by '7.5'.
6666666.667 + -8665.2x + x2 = 0

Move the constant term to the right:

Add '-6666666.667' to each side of the equation.
6666666.667 + -8665.2x + -6666666.667 + x2 = 0 + -6666666.667

Reorder the terms:
6666666.667 + -6666666.667 + -8665.2x + x2 = 0 + -6666666.667

Combine like terms: 6666666.667 + -6666666.667 = 0.000
0.000 + -8665.2x + x2 = 0 + -6666666.667
-8665.2x + x2 = 0 + -6666666.667

Combine like terms: 0 + -6666666.667 = -6666666.667
-8665.2x + x2 = -6666666.667

The x term is -8665.2x.  Take half its coefficient (-4332.6).
Square it (18771422.76) and add it to both sides.

Add '18771422.76' to each side of the equation.
-8665.2x + 18771422.76 + x2 = -6666666.667 + 18771422.76

Reorder the terms:
18771422.76 + -8665.2x + x2 = -6666666.667 + 18771422.76

Combine like terms: -6666666.667 + 18771422.76 = 12104756.093
18771422.76 + -8665.2x + x2 = 12104756.093

Factor a perfect square on the left side:
(x + -4332.6)(x + -4332.6) = 12104756.093

Calculate the square root of the right side: 3479.188999322

Break this problem into two subproblems by setting 
(x + -4332.6) equal to 3479.188999322 and -3479.188999322.


Subproblem 1
x + -4332.6 = 3479.188999322

Simplifying
x + -4332.6 = 3479.188999322

Reorder the terms:
-4332.6 + x = 3479.188999322

Solving
-4332.6 + x = 3479.188999322

Solving for variable 'x'.

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

Add '4332.6' to each side of the equation.
-4332.6 + 4332.6 + x = 3479.188999322 + 4332.6

Combine like terms: -4332.6 + 4332.6 = 0.0
0.0 + x = 3479.188999322 + 4332.6
x = 3479.188999322 + 4332.6

Combine like terms: 3479.188999322 + 4332.6 = 7811.788999322
x = 7811.788999322

Simplifying
x = 7811.788999322


Subproblem 2
x + -4332.6 = -3479.188999322

Simplifying
x + -4332.6 = -3479.188999322

Reorder the terms:
-4332.6 + x = -3479.188999322

Solving
-4332.6 + x = -3479.188999322

Solving for variable 'x'.

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

Add '4332.6' to each side of the equation.
-4332.6 + 4332.6 + x = -3479.188999322 + 4332.6

Combine like terms: -4332.6 + 4332.6 = 0.0
0.0 + x = -3479.188999322 + 4332.6
x = -3479.188999322 + 4332.6

Combine like terms: -3479.188999322 + 4332.6 = 853.411000678
x = 853.411000678

Simplifying
x = 853.411000678


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7811.788999322, 853.411000678}

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