7x^2+28x-120=0

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Solution for 7x^2+28x-120=0 equation: 


Simplifying
7x2 + 28x + -120 = 0

Reorder the terms:
-120 + 28x + 7x2 = 0

Solving
-120 + 28x + 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'.
-17.14285714 + 4x + x2 = 0

Move the constant term to the right:

Add '17.14285714' to each side of the equation.
-17.14285714 + 4x + 17.14285714 + x2 = 0 + 17.14285714

Reorder the terms:
-17.14285714 + 17.14285714 + 4x + x2 = 0 + 17.14285714

Combine like terms: -17.14285714 + 17.14285714 = 0.00000000
0.00000000 + 4x + x2 = 0 + 17.14285714
4x + x2 = 0 + 17.14285714

Combine like terms: 0 + 17.14285714 = 17.14285714
4x + x2 = 17.14285714

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 17.14285714 + 4

Reorder the terms:
4 + 4x + x2 = 17.14285714 + 4

Combine like terms: 17.14285714 + 4 = 21.14285714
4 + 4x + x2 = 21.14285714

Factor a perfect square on the left side:
(x + 2)(x + 2) = 21.14285714

Calculate the square root of the right side: 4.598136268

Break this problem into two subproblems by setting 
(x + 2) equal to 4.598136268 and -4.598136268.


Subproblem 1
x + 2 = 4.598136268

Simplifying
x + 2 = 4.598136268

Reorder the terms:
2 + x = 4.598136268

Solving
2 + x = 4.598136268

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = 4.598136268 + -2

Combine like terms: 2 + -2 = 0
0 + x = 4.598136268 + -2
x = 4.598136268 + -2

Combine like terms: 4.598136268 + -2 = 2.598136268
x = 2.598136268

Simplifying
x = 2.598136268


Subproblem 2
x + 2 = -4.598136268

Simplifying
x + 2 = -4.598136268

Reorder the terms:
2 + x = -4.598136268

Solving
2 + x = -4.598136268

Solving for variable 'x'.

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

Add '-2' to each side of the equation.
2 + -2 + x = -4.598136268 + -2

Combine like terms: 2 + -2 = 0
0 + x = -4.598136268 + -2
x = -4.598136268 + -2

Combine like terms: -4.598136268 + -2 = -6.598136268
x = -6.598136268

Simplifying
x = -6.598136268


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.598136268, -6.598136268}

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