5x^2+80x+230=0

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Solution for 5x^2+80x+230=0 equation: 


Simplifying
5x2 + 80x + 230 = 0

Reorder the terms:
230 + 80x + 5x2 = 0

Solving
230 + 80x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(46 + 16x + x2) = 0

Ignore the factor 5.

Subproblem 1
Set the factor '(46 + 16x + x2)' equal to zero and attempt to solve:

Simplifying
46 + 16x + x2 = 0

Solving
46 + 16x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-46' to each side of the equation.
46 + 16x + -46 + x2 = 0 + -46

Reorder the terms:
46 + -46 + 16x + x2 = 0 + -46

Combine like terms: 46 + -46 = 0
0 + 16x + x2 = 0 + -46
16x + x2 = 0 + -46

Combine like terms: 0 + -46 = -46
16x + x2 = -46

The x term is 16x.  Take half its coefficient (8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
16x + 64 + x2 = -46 + 64

Reorder the terms:
64 + 16x + x2 = -46 + 64

Combine like terms: -46 + 64 = 18
64 + 16x + x2 = 18

Factor a perfect square on the left side:
(x + 8)(x + 8) = 18

Calculate the square root of the right side: 4.242640687

Break this problem into two subproblems by setting 
(x + 8) equal to 4.242640687 and -4.242640687.


Subproblem 1
x + 8 = 4.242640687

Simplifying
x + 8 = 4.242640687

Reorder the terms:
8 + x = 4.242640687

Solving
8 + x = 4.242640687

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = 4.242640687 + -8

Combine like terms: 8 + -8 = 0
0 + x = 4.242640687 + -8
x = 4.242640687 + -8

Combine like terms: 4.242640687 + -8 = -3.757359313
x = -3.757359313

Simplifying
x = -3.757359313


Subproblem 2
x + 8 = -4.242640687

Simplifying
x + 8 = -4.242640687

Reorder the terms:
8 + x = -4.242640687

Solving
8 + x = -4.242640687

Solving for variable 'x'.

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

Add '-8' to each side of the equation.
8 + -8 + x = -4.242640687 + -8

Combine like terms: 8 + -8 = 0
0 + x = -4.242640687 + -8
x = -4.242640687 + -8

Combine like terms: -4.242640687 + -8 = -12.242640687
x = -12.242640687

Simplifying
x = -12.242640687


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.757359313, -12.242640687}
Solution
x = {-3.757359313, -12.242640687}

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