96x-x^2=960

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Solution for 96x-x^2=960 equation:


Simplifying
96x + -1x2 = 960

Solving
96x + -1x2 = 960

Solving for variable 'x'.

Reorder the terms:
-960 + 96x + -1x2 = 960 + -960

Combine like terms: 960 + -960 = 0
-960 + 96x + -1x2 = 0

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

Divide each side by '-1'.
960 + -96x + x2 = 0

Move the constant term to the right:

Add '-960' to each side of the equation.
960 + -96x + -960 + x2 = 0 + -960

Reorder the terms:
960 + -960 + -96x + x2 = 0 + -960

Combine like terms: 960 + -960 = 0
0 + -96x + x2 = 0 + -960
-96x + x2 = 0 + -960

Combine like terms: 0 + -960 = -960
-96x + x2 = -960

The x term is -96x.  Take half its coefficient (-48).
Square it (2304) and add it to both sides.

Add '2304' to each side of the equation.
-96x + 2304 + x2 = -960 + 2304

Reorder the terms:
2304 + -96x + x2 = -960 + 2304

Combine like terms: -960 + 2304 = 1344
2304 + -96x + x2 = 1344

Factor a perfect square on the left side:
(x + -48)(x + -48) = 1344

Calculate the square root of the right side: 36.66060556

Break this problem into two subproblems by setting 
(x + -48) equal to 36.66060556 and -36.66060556.

Subproblem 1

x + -48 = 36.66060556 Simplifying x + -48 = 36.66060556 Reorder the terms: -48 + x = 36.66060556 Solving -48 + x = 36.66060556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = 36.66060556 + 48 Combine like terms: -48 + 48 = 0 0 + x = 36.66060556 + 48 x = 36.66060556 + 48 Combine like terms: 36.66060556 + 48 = 84.66060556 x = 84.66060556 Simplifying x = 84.66060556

Subproblem 2

x + -48 = -36.66060556 Simplifying x + -48 = -36.66060556 Reorder the terms: -48 + x = -36.66060556 Solving -48 + x = -36.66060556 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '48' to each side of the equation. -48 + 48 + x = -36.66060556 + 48 Combine like terms: -48 + 48 = 0 0 + x = -36.66060556 + 48 x = -36.66060556 + 48 Combine like terms: -36.66060556 + 48 = 11.33939444 x = 11.33939444 Simplifying x = 11.33939444

Solution

The solution to the problem is based on the solutions from the subproblems. x = {84.66060556, 11.33939444}

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