115x-0.5x^2=400

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Solution for 115x-0.5x^2=400 equation:


Simplifying
115x + -0.5x2 = 400

Solving
115x + -0.5x2 = 400

Solving for variable 'x'.

Reorder the terms:
-400 + 115x + -0.5x2 = 400 + -400

Combine like terms: 400 + -400 = 0
-400 + 115x + -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'.
800 + -230x + x2 = 0

Move the constant term to the right:

Add '-800' to each side of the equation.
800 + -230x + -800 + x2 = 0 + -800

Reorder the terms:
800 + -800 + -230x + x2 = 0 + -800

Combine like terms: 800 + -800 = 0
0 + -230x + x2 = 0 + -800
-230x + x2 = 0 + -800

Combine like terms: 0 + -800 = -800
-230x + x2 = -800

The x term is -230x.  Take half its coefficient (-115).
Square it (13225) and add it to both sides.

Add '13225' to each side of the equation.
-230x + 13225 + x2 = -800 + 13225

Reorder the terms:
13225 + -230x + x2 = -800 + 13225

Combine like terms: -800 + 13225 = 12425
13225 + -230x + x2 = 12425

Factor a perfect square on the left side:
(x + -115)(x + -115) = 12425

Calculate the square root of the right side: 111.467484048

Break this problem into two subproblems by setting 
(x + -115) equal to 111.467484048 and -111.467484048.

Subproblem 1

x + -115 = 111.467484048 Simplifying x + -115 = 111.467484048 Reorder the terms: -115 + x = 111.467484048 Solving -115 + x = 111.467484048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '115' to each side of the equation. -115 + 115 + x = 111.467484048 + 115 Combine like terms: -115 + 115 = 0 0 + x = 111.467484048 + 115 x = 111.467484048 + 115 Combine like terms: 111.467484048 + 115 = 226.467484048 x = 226.467484048 Simplifying x = 226.467484048

Subproblem 2

x + -115 = -111.467484048 Simplifying x + -115 = -111.467484048 Reorder the terms: -115 + x = -111.467484048 Solving -115 + x = -111.467484048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '115' to each side of the equation. -115 + 115 + x = -111.467484048 + 115 Combine like terms: -115 + 115 = 0 0 + x = -111.467484048 + 115 x = -111.467484048 + 115 Combine like terms: -111.467484048 + 115 = 3.532515952 x = 3.532515952 Simplifying x = 3.532515952

Solution

The solution to the problem is based on the solutions from the subproblems. x = {226.467484048, 3.532515952}

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