510x-x^2=9600+9x

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Solution for 510x-x^2=9600+9x equation:


Simplifying
510x + -1x2 = 9600 + 9x

Solving
510x + -1x2 = 9600 + 9x

Solving for variable 'x'.

Reorder the terms:
-9600 + 510x + -9x + -1x2 = 9600 + 9x + -9600 + -9x

Combine like terms: 510x + -9x = 501x
-9600 + 501x + -1x2 = 9600 + 9x + -9600 + -9x

Reorder the terms:
-9600 + 501x + -1x2 = 9600 + -9600 + 9x + -9x

Combine like terms: 9600 + -9600 = 0
-9600 + 501x + -1x2 = 0 + 9x + -9x
-9600 + 501x + -1x2 = 9x + -9x

Combine like terms: 9x + -9x = 0
-9600 + 501x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
9600 + -501x + x2 = 0

Move the constant term to the right:

Add '-9600' to each side of the equation.
9600 + -501x + -9600 + x2 = 0 + -9600

Reorder the terms:
9600 + -9600 + -501x + x2 = 0 + -9600

Combine like terms: 9600 + -9600 = 0
0 + -501x + x2 = 0 + -9600
-501x + x2 = 0 + -9600

Combine like terms: 0 + -9600 = -9600
-501x + x2 = -9600

The x term is -501x.  Take half its coefficient (-250.5).
Square it (62750.25) and add it to both sides.

Add '62750.25' to each side of the equation.
-501x + 62750.25 + x2 = -9600 + 62750.25

Reorder the terms:
62750.25 + -501x + x2 = -9600 + 62750.25

Combine like terms: -9600 + 62750.25 = 53150.25
62750.25 + -501x + x2 = 53150.25

Factor a perfect square on the left side:
(x + -250.5)(x + -250.5) = 53150.25

Calculate the square root of the right side: 230.543379866

Break this problem into two subproblems by setting 
(x + -250.5) equal to 230.543379866 and -230.543379866.

Subproblem 1

x + -250.5 = 230.543379866 Simplifying x + -250.5 = 230.543379866 Reorder the terms: -250.5 + x = 230.543379866 Solving -250.5 + x = 230.543379866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250.5' to each side of the equation. -250.5 + 250.5 + x = 230.543379866 + 250.5 Combine like terms: -250.5 + 250.5 = 0.0 0.0 + x = 230.543379866 + 250.5 x = 230.543379866 + 250.5 Combine like terms: 230.543379866 + 250.5 = 481.043379866 x = 481.043379866 Simplifying x = 481.043379866

Subproblem 2

x + -250.5 = -230.543379866 Simplifying x + -250.5 = -230.543379866 Reorder the terms: -250.5 + x = -230.543379866 Solving -250.5 + x = -230.543379866 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '250.5' to each side of the equation. -250.5 + 250.5 + x = -230.543379866 + 250.5 Combine like terms: -250.5 + 250.5 = 0.0 0.0 + x = -230.543379866 + 250.5 x = -230.543379866 + 250.5 Combine like terms: -230.543379866 + 250.5 = 19.956620134 x = 19.956620134 Simplifying x = 19.956620134

Solution

The solution to the problem is based on the solutions from the subproblems. x = {481.043379866, 19.956620134}

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