104*x-0.03*x^2=100

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Solution for 104*x-0.03*x^2=100 equation:


Simplifying
104x + -0.03x2 = 100

Solving
104x + -0.03x2 = 100

Solving for variable 'x'.

Reorder the terms:
-100 + 104x + -0.03x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-100 + 104x + -0.03x2 = 0

Begin completing the square.  Divide all terms by
-0.03 the coefficient of the squared term: 

Divide each side by '-0.03'.
3333.333333 + -3466.666667x + x2 = 0

Move the constant term to the right:

Add '-3333.333333' to each side of the equation.
3333.333333 + -3466.666667x + -3333.333333 + x2 = 0 + -3333.333333

Reorder the terms:
3333.333333 + -3333.333333 + -3466.666667x + x2 = 0 + -3333.333333

Combine like terms: 3333.333333 + -3333.333333 = 0.000000
0.000000 + -3466.666667x + x2 = 0 + -3333.333333
-3466.666667x + x2 = 0 + -3333.333333

Combine like terms: 0 + -3333.333333 = -3333.333333
-3466.666667x + x2 = -3333.333333

The x term is -3466.666667x.  Take half its coefficient (-1733.333334).
Square it (3004444.447) and add it to both sides.

Add '3004444.447' to each side of the equation.
-3466.666667x + 3004444.447 + x2 = -3333.333333 + 3004444.447

Reorder the terms:
3004444.447 + -3466.666667x + x2 = -3333.333333 + 3004444.447

Combine like terms: -3333.333333 + 3004444.447 = 3001111.113667
3004444.447 + -3466.666667x + x2 = 3001111.113667

Factor a perfect square on the left side:
(x + -1733.333334)(x + -1733.333334) = 3001111.113667

Calculate the square root of the right side: 1732.371528763

Break this problem into two subproblems by setting 
(x + -1733.333334) equal to 1732.371528763 and -1732.371528763.

Subproblem 1

x + -1733.333334 = 1732.371528763 Simplifying x + -1733.333334 = 1732.371528763 Reorder the terms: -1733.333334 + x = 1732.371528763 Solving -1733.333334 + x = 1732.371528763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1733.333334' to each side of the equation. -1733.333334 + 1733.333334 + x = 1732.371528763 + 1733.333334 Combine like terms: -1733.333334 + 1733.333334 = 0.000000 0.000000 + x = 1732.371528763 + 1733.333334 x = 1732.371528763 + 1733.333334 Combine like terms: 1732.371528763 + 1733.333334 = 3465.704862763 x = 3465.704862763 Simplifying x = 3465.704862763

Subproblem 2

x + -1733.333334 = -1732.371528763 Simplifying x + -1733.333334 = -1732.371528763 Reorder the terms: -1733.333334 + x = -1732.371528763 Solving -1733.333334 + x = -1732.371528763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1733.333334' to each side of the equation. -1733.333334 + 1733.333334 + x = -1732.371528763 + 1733.333334 Combine like terms: -1733.333334 + 1733.333334 = 0.000000 0.000000 + x = -1732.371528763 + 1733.333334 x = -1732.371528763 + 1733.333334 Combine like terms: -1732.371528763 + 1733.333334 = 0.961805237 x = 0.961805237 Simplifying x = 0.961805237

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3465.704862763, 0.961805237}

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