(-.003X^2)+(2X)=-50

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Solution for (-.003X^2)+(2X)=-50 equation:


Simplifying
(-0.003X2) + (2X) = -50

Reorder the terms:
(2X) + (-0.003X2) = -50

Solving
(2X) + (-0.003X2) = -50

Solving for variable 'X'.

Reorder the terms:
50 + (2X) + (-0.003X2) = -50 + 50

Combine like terms: -50 + 50 = 0
50 + (2X) + (-0.003X2) = 0

Begin completing the square.  Divide all terms by
-0.003 the coefficient of the squared term: 

Divide each side by '-0.003'.
-16666.66667 + (-666.6666667X) + X2 = 0

Move the constant term to the right:

Add '16666.66667' to each side of the equation.
-16666.66667 + (-666.6666667X) + 16666.66667 + X2 = 0 + 16666.66667

Reorder the terms:
-16666.66667 + 16666.66667 + (-666.6666667X) + X2 = 0 + 16666.66667

Combine like terms: -16666.66667 + 16666.66667 = 0.00000
0.00000 + (-666.6666667X) + X2 = 0 + 16666.66667
(-666.6666667X) + X2 = 0 + 16666.66667

Combine like terms: 0 + 16666.66667 = 16666.66667
(-666.6666667X) + X2 = 16666.66667

The X term is (-666.6666667X).  Take half its coefficient (-333.3333334).
Square it (111111.1112) and add it to both sides.

Add '111111.1112' to each side of the equation.
(-666.6666667X) + 111111.1112 + X2 = 16666.66667 + 111111.1112

Reorder the terms:
111111.1112 + (-666.6666667X) + X2 = 16666.66667 + 111111.1112

Combine like terms: 16666.66667 + 111111.1112 = 127777.77787
111111.1112 + (-666.6666667X) + X2 = 127777.77787

Factor a perfect square on the left side:
((X) + -333.3333334)((X) + -333.3333334) = 127777.77787

Calculate the square root of the right side: 357.460176621

Break this problem into two subproblems by setting 
((X) + -333.3333334) equal to 357.460176621 and -357.460176621.

Subproblem 1

(X) + -333.3333334 = 357.460176621 Simplifying (X) + -333.3333334 = 357.460176621 X + -333.3333334 = 357.460176621 Reorder the terms: -333.3333334 + X = 357.460176621 Solving -333.3333334 + X = 357.460176621 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '333.3333334' to each side of the equation. -333.3333334 + 333.3333334 + X = 357.460176621 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + X = 357.460176621 + 333.3333334 X = 357.460176621 + 333.3333334 Combine like terms: 357.460176621 + 333.3333334 = 690.793510021 X = 690.793510021 Simplifying X = 690.793510021

Subproblem 2

(X) + -333.3333334 = -357.460176621 Simplifying (X) + -333.3333334 = -357.460176621 X + -333.3333334 = -357.460176621 Reorder the terms: -333.3333334 + X = -357.460176621 Solving -333.3333334 + X = -357.460176621 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '333.3333334' to each side of the equation. -333.3333334 + 333.3333334 + X = -357.460176621 + 333.3333334 Combine like terms: -333.3333334 + 333.3333334 = 0.0000000 0.0000000 + X = -357.460176621 + 333.3333334 X = -357.460176621 + 333.3333334 Combine like terms: -357.460176621 + 333.3333334 = -24.126843221 X = -24.126843221 Simplifying X = -24.126843221

Solution

The solution to the problem is based on the solutions from the subproblems. X = {690.793510021, -24.126843221}

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