3600=400x-3x^2

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Solution for 3600=400x-3x^2 equation:


Simplifying
3600 = 400x + -3x2

Solving
3600 = 400x + -3x2

Solving for variable 'x'.

Reorder the terms:
3600 + -400x + 3x2 = 400x + -400x + -3x2 + 3x2

Combine like terms: 400x + -400x = 0
3600 + -400x + 3x2 = 0 + -3x2 + 3x2
3600 + -400x + 3x2 = -3x2 + 3x2

Combine like terms: -3x2 + 3x2 = 0
3600 + -400x + 3x2 = 0

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

Divide each side by '3'.
1200 + -133.3333333x + x2 = 0

Move the constant term to the right:

Add '-1200' to each side of the equation.
1200 + -133.3333333x + -1200 + x2 = 0 + -1200

Reorder the terms:
1200 + -1200 + -133.3333333x + x2 = 0 + -1200

Combine like terms: 1200 + -1200 = 0
0 + -133.3333333x + x2 = 0 + -1200
-133.3333333x + x2 = 0 + -1200

Combine like terms: 0 + -1200 = -1200
-133.3333333x + x2 = -1200

The x term is -133.3333333x.  Take half its coefficient (-66.66666665).
Square it (4444.444442) and add it to both sides.

Add '4444.444442' to each side of the equation.
-133.3333333x + 4444.444442 + x2 = -1200 + 4444.444442

Reorder the terms:
4444.444442 + -133.3333333x + x2 = -1200 + 4444.444442

Combine like terms: -1200 + 4444.444442 = 3244.444442
4444.444442 + -133.3333333x + x2 = 3244.444442

Factor a perfect square on the left side:
(x + -66.66666665)(x + -66.66666665) = 3244.444442

Calculate the square root of the right side: 56.960024947

Break this problem into two subproblems by setting 
(x + -66.66666665) equal to 56.960024947 and -56.960024947.

Subproblem 1

x + -66.66666665 = 56.960024947 Simplifying x + -66.66666665 = 56.960024947 Reorder the terms: -66.66666665 + x = 56.960024947 Solving -66.66666665 + x = 56.960024947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = 56.960024947 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = 56.960024947 + 66.66666665 x = 56.960024947 + 66.66666665 Combine like terms: 56.960024947 + 66.66666665 = 123.626691597 x = 123.626691597 Simplifying x = 123.626691597

Subproblem 2

x + -66.66666665 = -56.960024947 Simplifying x + -66.66666665 = -56.960024947 Reorder the terms: -66.66666665 + x = -56.960024947 Solving -66.66666665 + x = -56.960024947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = -56.960024947 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = -56.960024947 + 66.66666665 x = -56.960024947 + 66.66666665 Combine like terms: -56.960024947 + 66.66666665 = 9.706641703 x = 9.706641703 Simplifying x = 9.706641703

Solution

The solution to the problem is based on the solutions from the subproblems. x = {123.626691597, 9.706641703}

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