7x^2-116x-240=0

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Solution for 7x^2-116x-240=0 equation: 


Simplifying
7x2 + -116x + -240 = 0

Reorder the terms:
-240 + -116x + 7x2 = 0

Solving
-240 + -116x + 7x2 = 0

Solving for variable 'x'.

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

Divide each side by '7'.
-34.28571429 + -16.57142857x + x2 = 0

Move the constant term to the right:

Add '34.28571429' to each side of the equation.
-34.28571429 + -16.57142857x + 34.28571429 + x2 = 0 + 34.28571429

Reorder the terms:
-34.28571429 + 34.28571429 + -16.57142857x + x2 = 0 + 34.28571429

Combine like terms: -34.28571429 + 34.28571429 = 0.00000000
0.00000000 + -16.57142857x + x2 = 0 + 34.28571429
-16.57142857x + x2 = 0 + 34.28571429

Combine like terms: 0 + 34.28571429 = 34.28571429
-16.57142857x + x2 = 34.28571429

The x term is -16.57142857x.  Take half its coefficient (-8.285714285).
Square it (68.65306121) and add it to both sides.

Add '68.65306121' to each side of the equation.
-16.57142857x + 68.65306121 + x2 = 34.28571429 + 68.65306121

Reorder the terms:
68.65306121 + -16.57142857x + x2 = 34.28571429 + 68.65306121

Combine like terms: 34.28571429 + 68.65306121 = 102.9387755
68.65306121 + -16.57142857x + x2 = 102.9387755

Factor a perfect square on the left side:
(x + -8.285714285)(x + -8.285714285) = 102.9387755

Calculate the square root of the right side: 10.145874802

Break this problem into two subproblems by setting 
(x + -8.285714285) equal to 10.145874802 and -10.145874802.


Subproblem 1
x + -8.285714285 = 10.145874802

Simplifying
x + -8.285714285 = 10.145874802

Reorder the terms:
-8.285714285 + x = 10.145874802

Solving
-8.285714285 + x = 10.145874802

Solving for variable 'x'.

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

Add '8.285714285' to each side of the equation.
-8.285714285 + 8.285714285 + x = 10.145874802 + 8.285714285

Combine like terms: -8.285714285 + 8.285714285 = 0.000000000
0.000000000 + x = 10.145874802 + 8.285714285
x = 10.145874802 + 8.285714285

Combine like terms: 10.145874802 + 8.285714285 = 18.431589087
x = 18.431589087

Simplifying
x = 18.431589087


Subproblem 2
x + -8.285714285 = -10.145874802

Simplifying
x + -8.285714285 = -10.145874802

Reorder the terms:
-8.285714285 + x = -10.145874802

Solving
-8.285714285 + x = -10.145874802

Solving for variable 'x'.

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

Add '8.285714285' to each side of the equation.
-8.285714285 + 8.285714285 + x = -10.145874802 + 8.285714285

Combine like terms: -8.285714285 + 8.285714285 = 0.000000000
0.000000000 + x = -10.145874802 + 8.285714285
x = -10.145874802 + 8.285714285

Combine like terms: -10.145874802 + 8.285714285 = -1.860160517
x = -1.860160517

Simplifying
x = -1.860160517


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.431589087, -1.860160517}

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