100x-0.5x^2=300

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Solution for 100x-0.5x^2=300 equation:


Simplifying
100x + -0.5x2 = 300

Solving
100x + -0.5x2 = 300

Solving for variable 'x'.

Reorder the terms:
-300 + 100x + -0.5x2 = 300 + -300

Combine like terms: 300 + -300 = 0
-300 + 100x + -0.5x2 = 0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
600 + -200x + x2 = 0

Move the constant term to the right:

Add '-600' to each side of the equation.
600 + -200x + -600 + x2 = 0 + -600

Reorder the terms:
600 + -600 + -200x + x2 = 0 + -600

Combine like terms: 600 + -600 = 0
0 + -200x + x2 = 0 + -600
-200x + x2 = 0 + -600

Combine like terms: 0 + -600 = -600
-200x + x2 = -600

The x term is -200x.  Take half its coefficient (-100).
Square it (10000) and add it to both sides.

Add '10000' to each side of the equation.
-200x + 10000 + x2 = -600 + 10000

Reorder the terms:
10000 + -200x + x2 = -600 + 10000

Combine like terms: -600 + 10000 = 9400
10000 + -200x + x2 = 9400

Factor a perfect square on the left side:
(x + -100)(x + -100) = 9400

Calculate the square root of the right side: 96.953597148

Break this problem into two subproblems by setting 
(x + -100) equal to 96.953597148 and -96.953597148.

Subproblem 1

x + -100 = 96.953597148 Simplifying x + -100 = 96.953597148 Reorder the terms: -100 + x = 96.953597148 Solving -100 + x = 96.953597148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = 96.953597148 + 100 Combine like terms: -100 + 100 = 0 0 + x = 96.953597148 + 100 x = 96.953597148 + 100 Combine like terms: 96.953597148 + 100 = 196.953597148 x = 196.953597148 Simplifying x = 196.953597148

Subproblem 2

x + -100 = -96.953597148 Simplifying x + -100 = -96.953597148 Reorder the terms: -100 + x = -96.953597148 Solving -100 + x = -96.953597148 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '100' to each side of the equation. -100 + 100 + x = -96.953597148 + 100 Combine like terms: -100 + 100 = 0 0 + x = -96.953597148 + 100 x = -96.953597148 + 100 Combine like terms: -96.953597148 + 100 = 3.046402852 x = 3.046402852 Simplifying x = 3.046402852

Solution

The solution to the problem is based on the solutions from the subproblems. x = {196.953597148, 3.046402852}

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