x^2+4x-340=0

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Solution for x^2+4x-340=0 equation: 


Simplifying
x2 + 4x + -340 = 0

Reorder the terms:
-340 + 4x + x2 = 0

Solving
-340 + 4x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '340' to each side of the equation.
-340 + 4x + 340 + x2 = 0 + 340

Reorder the terms:
-340 + 340 + 4x + x2 = 0 + 340

Combine like terms: -340 + 340 = 0
0 + 4x + x2 = 0 + 340
4x + x2 = 0 + 340

Combine like terms: 0 + 340 = 340
4x + x2 = 340

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 = 340 + 4

Reorder the terms:
4 + 4x + x2 = 340 + 4

Combine like terms: 340 + 4 = 344
4 + 4x + x2 = 344

Factor a perfect square on the left side:
(x + 2)(x + 2) = 344

Calculate the square root of the right side: 18.547236991

Break this problem into two subproblems by setting 
(x + 2) equal to 18.547236991 and -18.547236991.


Subproblem 1
x + 2 = 18.547236991

Simplifying
x + 2 = 18.547236991

Reorder the terms:
2 + x = 18.547236991

Solving
2 + x = 18.547236991

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 = 18.547236991 + -2

Combine like terms: 2 + -2 = 0
0 + x = 18.547236991 + -2
x = 18.547236991 + -2

Combine like terms: 18.547236991 + -2 = 16.547236991
x = 16.547236991

Simplifying
x = 16.547236991


Subproblem 2
x + 2 = -18.547236991

Simplifying
x + 2 = -18.547236991

Reorder the terms:
2 + x = -18.547236991

Solving
2 + x = -18.547236991

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 = -18.547236991 + -2

Combine like terms: 2 + -2 = 0
0 + x = -18.547236991 + -2
x = -18.547236991 + -2

Combine like terms: -18.547236991 + -2 = -20.547236991
x = -20.547236991

Simplifying
x = -20.547236991


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.547236991, -20.547236991}

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