8x^2+94x+230=0

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Solution for 8x^2+94x+230=0 equation: 


Simplifying
8x2 + 94x + 230 = 0

Reorder the terms:
230 + 94x + 8x2 = 0

Solving
230 + 94x + 8x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(115 + 47x + 4x2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(115 + 47x + 4x2)' equal to zero and attempt to solve:

Simplifying
115 + 47x + 4x2 = 0

Solving
115 + 47x + 4x2 = 0

Begin completing the square.  Divide all terms by
4 the coefficient of the squared term: 

Divide each side by '4'.
28.75 + 11.75x + x2 = 0

Move the constant term to the right:

Add '-28.75' to each side of the equation.
28.75 + 11.75x + -28.75 + x2 = 0 + -28.75

Reorder the terms:
28.75 + -28.75 + 11.75x + x2 = 0 + -28.75

Combine like terms: 28.75 + -28.75 = 0.00
0.00 + 11.75x + x2 = 0 + -28.75
11.75x + x2 = 0 + -28.75

Combine like terms: 0 + -28.75 = -28.75
11.75x + x2 = -28.75

The x term is 11.75x.  Take half its coefficient (5.875).
Square it (34.515625) and add it to both sides.

Add '34.515625' to each side of the equation.
11.75x + 34.515625 + x2 = -28.75 + 34.515625

Reorder the terms:
34.515625 + 11.75x + x2 = -28.75 + 34.515625

Combine like terms: -28.75 + 34.515625 = 5.765625
34.515625 + 11.75x + x2 = 5.765625

Factor a perfect square on the left side:
(x + 5.875)(x + 5.875) = 5.765625

Calculate the square root of the right side: 2.401171589

Break this problem into two subproblems by setting 
(x + 5.875) equal to 2.401171589 and -2.401171589.


Subproblem 1
x + 5.875 = 2.401171589

Simplifying
x + 5.875 = 2.401171589

Reorder the terms:
5.875 + x = 2.401171589

Solving
5.875 + x = 2.401171589

Solving for variable 'x'.

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

Add '-5.875' to each side of the equation.
5.875 + -5.875 + x = 2.401171589 + -5.875

Combine like terms: 5.875 + -5.875 = 0.000
0.000 + x = 2.401171589 + -5.875
x = 2.401171589 + -5.875

Combine like terms: 2.401171589 + -5.875 = -3.473828411
x = -3.473828411

Simplifying
x = -3.473828411


Subproblem 2
x + 5.875 = -2.401171589

Simplifying
x + 5.875 = -2.401171589

Reorder the terms:
5.875 + x = -2.401171589

Solving
5.875 + x = -2.401171589

Solving for variable 'x'.

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

Add '-5.875' to each side of the equation.
5.875 + -5.875 + x = -2.401171589 + -5.875

Combine like terms: 5.875 + -5.875 = 0.000
0.000 + x = -2.401171589 + -5.875
x = -2.401171589 + -5.875

Combine like terms: -2.401171589 + -5.875 = -8.276171589
x = -8.276171589

Simplifying
x = -8.276171589


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-3.473828411, -8.276171589}
Solution
x = {-3.473828411, -8.276171589}

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