104=.5[(360-x)*-x]

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Solution for 104=.5[(360-x)*-x] equation:


Simplifying
104 = 0.5[(360 + -1x) * -1x]

Reorder the terms for easier multiplication:
104 = 0.5[-1x(360 + -1x)]
104 = 0.5[(360 * -1x + -1x * -1x)]
104 = 0.5[(-360x + 1x2)]
104 = [-360x * 0.5 + 1x2 * 0.5]
104 = [-180x + 0.5x2]

Solving
104 = -180x + 0.5x2

Solving for variable 'x'.

Reorder the terms:
104 + 180x + -0.5x2 = -180x + 180x + 0.5x2 + -0.5x2

Combine like terms: -180x + 180x = 0
104 + 180x + -0.5x2 = 0 + 0.5x2 + -0.5x2
104 + 180x + -0.5x2 = 0.5x2 + -0.5x2

Combine like terms: 0.5x2 + -0.5x2 = 0.0
104 + 180x + -0.5x2 = 0.0

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

Divide each side by '-0.5'.
-208 + -360x + x2 = 0

Move the constant term to the right:

Add '208' to each side of the equation.
-208 + -360x + 208 + x2 = 0 + 208

Reorder the terms:
-208 + 208 + -360x + x2 = 0 + 208

Combine like terms: -208 + 208 = 0
0 + -360x + x2 = 0 + 208
-360x + x2 = 0 + 208

Combine like terms: 0 + 208 = 208
-360x + x2 = 208

The x term is -360x.  Take half its coefficient (-180).
Square it (32400) and add it to both sides.

Add '32400' to each side of the equation.
-360x + 32400 + x2 = 208 + 32400

Reorder the terms:
32400 + -360x + x2 = 208 + 32400

Combine like terms: 208 + 32400 = 32608
32400 + -360x + x2 = 32608

Factor a perfect square on the left side:
(x + -180)(x + -180) = 32608

Calculate the square root of the right side: 180.576853445

Break this problem into two subproblems by setting 
(x + -180) equal to 180.576853445 and -180.576853445.

Subproblem 1

x + -180 = 180.576853445 Simplifying x + -180 = 180.576853445 Reorder the terms: -180 + x = 180.576853445 Solving -180 + x = 180.576853445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + x = 180.576853445 + 180 Combine like terms: -180 + 180 = 0 0 + x = 180.576853445 + 180 x = 180.576853445 + 180 Combine like terms: 180.576853445 + 180 = 360.576853445 x = 360.576853445 Simplifying x = 360.576853445

Subproblem 2

x + -180 = -180.576853445 Simplifying x + -180 = -180.576853445 Reorder the terms: -180 + x = -180.576853445 Solving -180 + x = -180.576853445 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '180' to each side of the equation. -180 + 180 + x = -180.576853445 + 180 Combine like terms: -180 + 180 = 0 0 + x = -180.576853445 + 180 x = -180.576853445 + 180 Combine like terms: -180.576853445 + 180 = -0.576853445 x = -0.576853445 Simplifying x = -0.576853445

Solution

The solution to the problem is based on the solutions from the subproblems. x = {360.576853445, -0.576853445}

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