240+10x-x^2=0

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Solution for 240+10x-x^2=0 equation: 


Simplifying
240 + 10x + -1x2 = 0

Solving
240 + 10x + -1x2 = 0

Solving for variable 'x'.

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

Divide each side by '-1'.
-240 + -10x + x2 = 0

Move the constant term to the right:

Add '240' to each side of the equation.
-240 + -10x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + -10x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + -10x + x2 = 0 + 240
-10x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
-10x + x2 = 240

The x term is -10x.  Take half its coefficient (-5).
Square it (25) and add it to both sides.

Add '25' to each side of the equation.
-10x + 25 + x2 = 240 + 25

Reorder the terms:
25 + -10x + x2 = 240 + 25

Combine like terms: 240 + 25 = 265
25 + -10x + x2 = 265

Factor a perfect square on the left side:
(x + -5)(x + -5) = 265

Calculate the square root of the right side: 16.278820596

Break this problem into two subproblems by setting 
(x + -5) equal to 16.278820596 and -16.278820596.


Subproblem 1
x + -5 = 16.278820596

Simplifying
x + -5 = 16.278820596

Reorder the terms:
-5 + x = 16.278820596

Solving
-5 + x = 16.278820596

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x = 16.278820596 + 5

Combine like terms: -5 + 5 = 0
0 + x = 16.278820596 + 5
x = 16.278820596 + 5

Combine like terms: 16.278820596 + 5 = 21.278820596
x = 21.278820596

Simplifying
x = 21.278820596


Subproblem 2
x + -5 = -16.278820596

Simplifying
x + -5 = -16.278820596

Reorder the terms:
-5 + x = -16.278820596

Solving
-5 + x = -16.278820596

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '5' to each side of the equation.
-5 + 5 + x = -16.278820596 + 5

Combine like terms: -5 + 5 = 0
0 + x = -16.278820596 + 5
x = -16.278820596 + 5

Combine like terms: -16.278820596 + 5 = -11.278820596
x = -11.278820596

Simplifying
x = -11.278820596


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {21.278820596, -11.278820596}

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