4x^2+120x+680=0

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Solution for 4x^2+120x+680=0 equation: 


Simplifying
4x2 + 120x + 680 = 0

Reorder the terms:
680 + 120x + 4x2 = 0

Solving
680 + 120x + 4x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(170 + 30x + x2) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(170 + 30x + x2)' equal to zero and attempt to solve:

Simplifying
170 + 30x + x2 = 0

Solving
170 + 30x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-170' to each side of the equation.
170 + 30x + -170 + x2 = 0 + -170

Reorder the terms:
170 + -170 + 30x + x2 = 0 + -170

Combine like terms: 170 + -170 = 0
0 + 30x + x2 = 0 + -170
30x + x2 = 0 + -170

Combine like terms: 0 + -170 = -170
30x + x2 = -170

The x term is 30x.  Take half its coefficient (15).
Square it (225) and add it to both sides.

Add '225' to each side of the equation.
30x + 225 + x2 = -170 + 225

Reorder the terms:
225 + 30x + x2 = -170 + 225

Combine like terms: -170 + 225 = 55
225 + 30x + x2 = 55

Factor a perfect square on the left side:
(x + 15)(x + 15) = 55

Calculate the square root of the right side: 7.416198487

Break this problem into two subproblems by setting 
(x + 15) equal to 7.416198487 and -7.416198487.


Subproblem 1
x + 15 = 7.416198487

Simplifying
x + 15 = 7.416198487

Reorder the terms:
15 + x = 7.416198487

Solving
15 + x = 7.416198487

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = 7.416198487 + -15

Combine like terms: 15 + -15 = 0
0 + x = 7.416198487 + -15
x = 7.416198487 + -15

Combine like terms: 7.416198487 + -15 = -7.583801513
x = -7.583801513

Simplifying
x = -7.583801513


Subproblem 2
x + 15 = -7.416198487

Simplifying
x + 15 = -7.416198487

Reorder the terms:
15 + x = -7.416198487

Solving
15 + x = -7.416198487

Solving for variable 'x'.

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

Add '-15' to each side of the equation.
15 + -15 + x = -7.416198487 + -15

Combine like terms: 15 + -15 = 0
0 + x = -7.416198487 + -15
x = -7.416198487 + -15

Combine like terms: -7.416198487 + -15 = -22.416198487
x = -22.416198487

Simplifying
x = -22.416198487


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-7.583801513, -22.416198487}
Solution
x = {-7.583801513, -22.416198487}

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