x^2+5x-340=0

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Solution for x^2+5x-340=0 equation: 


Simplifying
x2 + 5x + -340 = 0

Reorder the terms:
-340 + 5x + x2 = 0

Solving
-340 + 5x + 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 + 5x + 340 + x2 = 0 + 340

Reorder the terms:
-340 + 340 + 5x + x2 = 0 + 340

Combine like terms: -340 + 340 = 0
0 + 5x + x2 = 0 + 340
5x + x2 = 0 + 340

Combine like terms: 0 + 340 = 340
5x + x2 = 340

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 340 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 340 + 6.25

Combine like terms: 340 + 6.25 = 346.25
6.25 + 5x + x2 = 346.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 346.25

Calculate the square root of the right side: 18.607794066

Break this problem into two subproblems by setting 
(x + 2.5) equal to 18.607794066 and -18.607794066.


Subproblem 1
x + 2.5 = 18.607794066

Simplifying
x + 2.5 = 18.607794066

Reorder the terms:
2.5 + x = 18.607794066

Solving
2.5 + x = 18.607794066

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 18.607794066 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 18.607794066 + -2.5
x = 18.607794066 + -2.5

Combine like terms: 18.607794066 + -2.5 = 16.107794066
x = 16.107794066

Simplifying
x = 16.107794066


Subproblem 2
x + 2.5 = -18.607794066

Simplifying
x + 2.5 = -18.607794066

Reorder the terms:
2.5 + x = -18.607794066

Solving
2.5 + x = -18.607794066

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -18.607794066 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -18.607794066 + -2.5
x = -18.607794066 + -2.5

Combine like terms: -18.607794066 + -2.5 = -21.107794066
x = -21.107794066

Simplifying
x = -21.107794066


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {16.107794066, -21.107794066}

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