1x^2+10x-240=0

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Solution for 1x^2+10x-240=0 equation: 


Simplifying
1x2 + 10x + -240 = 0

Reorder the terms:
-240 + 10x + 1x2 = 0

Solving
-240 + 10x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

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 = 11.278820596
x = 11.278820596

Simplifying
x = 11.278820596


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 = -21.278820596
x = -21.278820596

Simplifying
x = -21.278820596


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

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