x^2+7x-240=0

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Solution for x^2+7x-240=0 equation:


Simplifying
x2 + 7x + -240 = 0

Reorder the terms:
-240 + 7x + x2 = 0

Solving
-240 + 7x + x2 = 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 + 7x + 240 + x2 = 0 + 240

Reorder the terms:
-240 + 240 + 7x + x2 = 0 + 240

Combine like terms: -240 + 240 = 0
0 + 7x + x2 = 0 + 240
7x + x2 = 0 + 240

Combine like terms: 0 + 240 = 240
7x + x2 = 240

The x term is 7x.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7x + 12.25 + x2 = 240 + 12.25

Reorder the terms:
12.25 + 7x + x2 = 240 + 12.25

Combine like terms: 240 + 12.25 = 252.25
12.25 + 7x + x2 = 252.25

Factor a perfect square on the left side:
(x + 3.5)(x + 3.5) = 252.25

Calculate the square root of the right side: 15.882380174

Break this problem into two subproblems by setting 
(x + 3.5) equal to 15.882380174 and -15.882380174.


Subproblem 1
x + 3.5 = 15.882380174

Simplifying
x + 3.5 = 15.882380174

Reorder the terms:
3.5 + x = 15.882380174

Solving
3.5 + x = 15.882380174

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = 15.882380174 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = 15.882380174 + -3.5
x = 15.882380174 + -3.5

Combine like terms: 15.882380174 + -3.5 = 12.382380174
x = 12.382380174

Simplifying
x = 12.382380174


Subproblem 2
x + 3.5 = -15.882380174

Simplifying
x + 3.5 = -15.882380174

Reorder the terms:
3.5 + x = -15.882380174

Solving
3.5 + x = -15.882380174

Solving for variable 'x'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + x = -15.882380174 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + x = -15.882380174 + -3.5
x = -15.882380174 + -3.5

Combine like terms: -15.882380174 + -3.5 = -19.382380174
x = -19.382380174

Simplifying
x = -19.382380174


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.382380174, -19.382380174}

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